Section 2.1.0 - Introductory Writeups
Section 2.1.0.1 - Basic Writeups
Section 2.1.0.1.1 - Part 1 - Katariya - Statistics Introduction
Section 2.1.0.1.2 - Part 2 - Wikipedia - Statistics
Section 2.1.0.1.3 - Part 3 - Wikibooks - Statistics
Section 2.1.0.1.4 - Part 4 - Wikipedia - Glossary of Probability and Statistics
Section 2.1.0.2 - Detailed Writeups
Section 2.1.0.2.1 - Part 1 - MIT - Statistics Cheatsheet
Section 2.1.0.2.2 - Part 2 - Keone Hon - Introduction to Statistics
Section 2.1.0.2.3 - Part 3 - David M. Lane - Introduction to Statistics
Section 2.1.0.2.4 - Part 4 - Joseph C. Watkins - An Introduction to the Science of Statistics
Section 2.1.0.2.5 - Part 5 - Prasanna Sahoo - Probability and Mathematical Statistics
Section 2.1.0.2.6 - Part 6 - Louisville - Probability and Mathematical Statistics
Section 2.1.0.2.7 - Part 7 - Louisville - Probability and Mathematical Statistics
Section 2.1.0.2.8 - Part 8 - Allen B. Downey - Think Stats I
Section 2.1.0.2.9 - Part 9 - Allen B. Downey - Think Stats 2nd Edition
Section 2.1.0.3 - Code
Section 2.1.0.3.1 - Part 1 - Rouse Guy - Intro2Stats
Section 2.1.0.3.2 - Part 2 - Sujit Pal - Think Stats Solutions(Check Allen Downey's book above)
Section 2.1.0.3.3 - Part 3 - Allen Downey - Think Stats 2 Code
Section 2.1.0.4 - Videos
Section 2.1.0.4.1 - Part 1 - MIT - Courseware on Statistics
Section 2.1.0.4.2 - Part 2 - Khan Academy - Statistics
Section 2.1.0.4.3 - Part 3 - Dr. Nic's - Series on Statistics
Section 2.1.1 - Inferential Statistics in Machine Learning
Section 2.1.1.0 - Basic Writeup - Katariya - Inferential Statistics in Machine Learning
Section 2.1.1.1 - Statistical Classification
Section 2.1.1.2 - Regression Analysis
Section 2.1.1.3 - Bayesian Statistics
Section 2.1.2 - Some Statistical Fundamentals
Section 2.1.2.0 - Basic Writeup - Katariya - Statistical Fundamentals
Section 2.1.2.1 - Mean
Section 2.1.2.2 - Median
Section 2.1.2.3 - Mode
Section 2.1.2.4 - Random(Stochastic) Variable
Section 2.1.2.5 - Univariate Random Variable
Section 2.1.2.6 - Multivariate Random Variable or Random Vector
Section 2.1.2.7 - Probability Mass Function - pmf- (Probability for Discrete Random)
Section 2.1.2.8 - Probablity Density Function - pdf- (Limit Integrated for Continuous Random)
Section 2.1.2.9 - Cummulative Distribution Function (CDF)
Section 2.1.2.10 - Skewness
Section 2.1.2.11 - Kutosis
Section 2.1.2.12 - Entropy
Section 2.1.2.13 - Moment Generating Function - MGF
Section 2.1.2.14 - Characteristic Function
Section 2.1.2.15 - Probability Generating Function - PGF
Section 2.1.2.16 - Fisher Information
Section 2.1.2.17 - Expected Value
Section 2.1.2.18 - Deviation
Section 2.1.2.19 - Variance
Section 2.1.2.20 - Covariance
Section 2.1.2.21 - Standard Deviation
Section 2.1.2.22 - Average absolute deviation
Section 2.1.2.23 - Bootstrapping
Section 2.1.2.23.0 - Basic Writeup - Wikipedia - Bootstrapping (Statistics)
Section 2.1.2.23.1 - Case Resampling
Section 2.1.2.23.2 - Bayesian bootstrap
Section 2.1.2.23.3 - Smooth bootstrap
Section 2.1.2.23.4 - Parametric bootstrap
Section 2.1.2.23.5 - Resampling residuals
Section 2.1.2.23.6 - Gaussian process regression bootstrap
Section 2.1.2.23.7 - Wild bootstrap
Section 2.1.2.23.8 - Block bootstrap
Section 2.1.2.24 - Statistical Sampling
Section 2.1.2.24.0 - Basic Writeup - Wikipedia - Sampling (Statistics)
Section 2.1.2.24.1 - Sampling Frame
Section 2.1.2.24.1.0 - Basic Writeup - Wikipedia - Sampling Frame
Section 2.1.2.24.1.1 - Probability Sampling
Section 2.1.2.24.1.2 - Non-Probability Sampling
Section 2.1.2.24.2 - Sampling Methods
Section 2.1.2.24.2.0 - Basic Writeup - Wikipedia - Sampling Methods
Section 2.1.2.24.2.1 - Simple Random Sampling
Section 2.1.2.24.2.2 - Systematic Sampling
Section 2.1.2.24.2.3 - Stratified Sampling
Section 2.1.2.24.2.4 - Probability-proportional-to-size sampling
Section 2.1.2.24.2.5 - Cluster Sampling
Section 2.1.2.24.2.6 - Quota Sampling
Section 2.1.2.24.2.7 - Minimax Sampling
Section 2.1.2.24.2.8 - Accidental Sampling
Section 2.1.2.24.2.9 - Voluntary Sampling
Section 2.1.2.24.2.10 - Line-intercept Sampling
Section 2.1.2.24.2.11 - Panel Sampling
Section 2.1.2.24.2.12 - Snowball Sampling
Section 2.1.2.24.2.13 - Theoretical Sampling
Section 2.1.3 - Types of Statistical Models
Section 2.1.3.0 - Basic Writeup - Katariya - Types of Statistical Models
Section 2.1.3.1 - Discriminative Statistical Modeling
Section 2.1.3.2 - Generative Statistical Modeling
Section 2.1.3.3 - Probabalistic Graphical Statistical Modeling
Section 2.1.4 - Estimators and Estimation Theory
Section 2.1.4.0 - Basic Writeup - Katariya - Estimators and Estimation Theory
Section 2.1.4.1 - Bounding Variance or Divergence in Estimation
Section 2.1.4.1.0 - Basic Writeup - Paniniski - Estimation Theory
Section 2.1.4.1.1 - Cramér–Rao bound
Section 2.1.4.1.2 - Chapman–Robbins bound
Section 2.1.4.1.3 - Kullback's inequality
Section 2.1.4.1.4 - Brascamp–Lieb inequality
Section 2.1.4.2 - Regression Analysis Techniques Based Estimation
Section 2.1.4.2.0 - Basic Writeup - Katariya - Regression Analysis Techniques
Section 2.1.4.2.1 - Least Squares
Section 2.1.4.2.1.0 - Basic Writeup - Wikipedia - Least Squares
Section 2.1.4.2.1.1 - Linear Least Squares Estimators
Section 2.1.4.2.1.1.0 - Basic Writeup - Wikipedia - Linear Least Squares
Section 2.1.4.2.1.1.1 - Ordinary Least Squares Estimator
Section 2.1.4.2.1.1.2 - Weighted Least Squares Estimator
Section 2.1.4.2.1.1.3 - Generalized Least Squares Estimator
Section 2.1.4.2.1.1.4 - Iteratively Weighted Least Squares Estimator
Section 2.1.4.2.1.1.5 - Instrumental Variables Regression
Section 2.1.4.2.1.1.6 - Total Least Squares
Section 2.1.4.2.1.2 - Non-Linear Least Squares Estimators
Section 2.1.4.2.1.3 - Partial Least Squares Estimators
Section 2.1.4.2.1.4 - Non-Negative Least Squares Estimators
Section 2.1.4.2.1.5 - Regularized Least Squares Estimators
Section 2.1.4.2.1.6 - Polynomial Least Squares Estimators
Section 2.1.4.2.2 - Least Absolute Deviation (LAD) Regression
Section 2.1.4.2.3 - Lasso (least absolute shrinkage and selection operator) Regression
Section 2.1.4.2.4 - Bayesian Linear Regression
Section 2.1.4.2.5 - Bayesian Multivariate Linear Regression
Section 2.1.4.2.6 - Quantile Regression
Section 2.1.4.3 - Bayesian Statistical Techniques Based Estimation
Section 2.1.4.3.1 - Bayesian Linear Regression
Section 2.1.4.3.2 - Bayesian Multivariate Linear Regression
Section 2.1.4.3.3 - Bayes Estimators
Section 2.1.4.3.4 - Maximum a posteriori (MAP)
Section 2.1.4.3.5 - Markov Chain Monte Carlo (MCMC)
Section 2.1.4.3.5.0 - Introductory Writeups
Section 2.1.4.3.5.0.1 - Basic Writeup - Katariya - Markov Chain Monte Carlo
Section 2.1.4.3.5.0.2 - Detailed Writeup - Wikipedia - Markov Chain Monte Carlo
Section 2.1.4.3.5.1 - Markov Chain Monte Carlo with Examples
Section 2.1.4.4 - Minimum Mean Square Error Techniques Based Estimation
Section 2.1.4.4.0 - Basic Writeup - Wikipedia - Minimum Mean Square Error
Section 2.1.4.4.1 - Linear MMSE
Section 2.1.4.4.2 - Sequential Linear MMSE
Section 2.1.4.4.3 - Kalman Filter
Section 2.1.4.4.4 - Weiner Filter
Section 2.1.4.5 - Maximum Likelihood Estimators
Section 2.1.4.5.0 - Introductory Writeups
Section 2.1.4.5.0.1 - Basic Writeup - Katariya - Maximun Likelihood Estimators
Section 2.1.4.5.0.2 - Detailed Writeup - Wikipdeia - Maximum Likelihood Estimation
Section 2.1.4.6 - Adaptive Estimation
Section 2.1.4.7 - Method of Moments Estimators
Section 2.1.4.8 - The Theil-Sen Estimator
Section 2.1.4.9 - Prediction Error Method
Section 2.1.4.10 - Minimum Variance Unbiased Estimator (MVUE)
Section 2.1.4.11 - Best Linear Unbiased Estimator (BLLUE) - Gauss Markov Theorem
Section 2.1.4.12 - Estimator Bias
Section 2.1.4.12.0 - Estimator Bias
Section 2.1.4.12.1 - Median-unbiased Estimators
Section 2.1.4.12.2 - Bayesian View
Section 2.1.4.13 - Spectral Density Estimation
Section 2.1.4.13.0 - Introductory Writeups
Section 2.1.4.13.0.1 - Basic Writeup - Katariya - Spectral Density Estimations
Section 2.1.4.13.0.2 - Detailed Writeup - Wikipedia - Spectral Density Estimation
Section 2.1.4.13.1 - Spectral Density Estimation Techniques
Section 2.1.4.13.1.0 - Basic Writeup - Wikipedia - Spectal Density Estimation Techniques
Section 2.1.4.13.1.1 - Non-Parametric Spectral Density Estimation Techinques
Section 2.1.4.13.1.1.0 - Basic Writeup - TAMU - Nonparametric Spectal Density Estimation
Section 2.1.4.13.1.1.1 - Periodogram
Section 2.1.4.13.1.1.2 - Bartlett's method
Section 2.1.4.13.1.1.3 - Welch's method
Section 2.1.4.13.1.1.4 - Multitaper
Section 2.1.4.13.1.1.5 - Least Squares Spectral Analysis
Section 2.1.4.13.1.1.6 - Non-uniform discrete Fourier transform
Section 2.1.4.13.1.1.7 - Singular Spectrum Analysis
Section 2.1.4.13.1.1.8 - Short-time Fourier transform
Section 2.1.4.13.1.1.9 - Critical filter
Section 2.1.4.13.1.2 - Parametric Spectral Density Estimation Techniques
Section 2.1.4.13.1.2.0 - Basic Writeup - Wikipedia - Parametric Spectral Density Estimation Techniques
Section 2.1.4.13.1.2.1 - Autoregressive model (AR) estimation
Section 2.1.4.13.1.2.2 - Moving-average model (MA) estimation
Section 2.1.4.13.1.2.3 - Autoregressive moving average (ARMA) estimation
Section 2.1.4.13.1.2.4 - MUltiple SIgnal Classification (MUSIC)
Section 2.1.4.13.1.2.5 - Maximum entropy spectral estimation
Section 2.1.5 - Statistical Hypothesis Testing
Section 2.1.5.0 - Basic Writeup - Wikipedia - Statistical Hypothesis Testing
Section 2.1.5.1 - Z-Test (Normal)
Section 2.1.5.2 - Students t-test
Section 2.1.5.3 - F-Test
Section 2.1.5.4 - Goodness of Fit
Section 2.1.5.4.0 - Basic Writeup - Wikipedia - Goodness Of Fit
Section 2.1.5.4.1 - Chi-squared
Section 2.1.5.4.2 - G-Test
Section 2.1.5.4.3 - Kolmogorov–Smirnov
Section 2.1.5.4.4 - Anderson–Darling
Section 2.1.5.4.5 - Lilliefors
Section 2.1.5.4.6 - Jarque–Bera
Section 2.1.5.4.7 - Normality (Shapiro–Wilk)
Section 2.1.5.4.8 - Likelihood Ratio Test
Section 2.1.5.4.9 - Modal Selection
Section 2.1.5.4.10 - Cross Validation
Section 2.1.5.4.11 - Cross Validation
Section 2.1.5.4.12 - Model Selection Criteria
Section 2.1.5.4.12.0 Basic Writeup - Wikipedia - Model Selection
Section 2.1.5.4.12.1 Akaike information criterion
Section 2.1.5.4.12.2 Bayesian information criterion
Section 2.1.5.5 - Rank Statistics
Section 2.1.5.5.0 - Basic Writeup - Wikipedia - Rank Statistics
Section 2.1.5.5.1 - Sign Test
Section 2.1.5.5.2 - Signed Rank (Wilcox)
Section 2.1.5.5.3 - Rank Sum (Mann-Whitney)
Section 2.1.5.5.4 - Non-Parametric ANOVA (1-way Kruskal-Wallis)
Section 2.1.5.5.5 - 2-way (Friedman)
Section 2.1.5.5.6 - Ordered alternative (Jonckheere–Terpstra)
Section 2.1.6 - Statistical Modeling
Section 2.1.6.0 - Basic Writeup - Wikipedia - Statistical Modeling
Section 2.1.6.1 - Regression Analysis and Modeling
Section 2.1.6.1.0 - Basic Writeup - Wikipedia - Regression Analysis
Section 2.1.6.1.1 - Linear Regression
Section 2.1.6.1.2 - Simple and Multiple Linear Regression
Section 2.1.6.1.3 - Polynomial Regression
Section 2.1.6.1.4 - General linear or Multivariate model
Section 2.1.6.1.5 - Generalized Linear Model
Section 2.1.6.1.6 - Discrete choice
Section 2.1.6.1.7 - Logistic regression
Section 2.1.6.1.8 - Multinomial logistic regression
Section 2.1.6.1.9 - Mixed logit
Section 2.1.6.1.10 - Probit Model
Section 2.1.6.1.11 - Multinomial Probit Model
Section 2.1.6.1.12 - Ordered Logit
Section 2.1.6.1.13 - Ordered Probit
Section 2.1.6.1.14 - Poisson Regression
Section 2.1.6.1.15 - Ordinal Regression
Section 2.1.6.1.16 Multilevel model
Section 2.1.6.1.17 - Fixed Effects Model
Section 2.1.6.1.18 - Random Effects Model
Section 2.1.6.1.19 - Mixed Model
Section 2.1.6.1.20 - Nonlinear Regression
Section 2.1.6.1.21 - Nonparametric Regression
Section 2.1.6.1.22 - Semi parametric Regression
Section 2.1.6.1.23 - Robust Regression
Section 2.1.6.1.24 - Quantile Regression
Section 2.1.6.1.25 - Isotonic Regression
Section 2.1.6.1.26 - Principal Components Regression
Section 2.1.6.1.27 - Least Angle Regression
Section 2.1.6.1.28 - Local Regression
Section 2.1.6.1.29 - Segmented Regression
Section 2.1.6.1.30 - Errors In Variables Model
Section 2.1.6.2 - System Indentification
Section 2.1.6.2.0 - Basic Writeup - Wikipedia - System Identification
Section 2.1.6.2.1 - Nonlinear System Identification
Section 2.1.6.2.1.0 - Basic Writeup - Wikipedia - NonLinear System Identification
Section 2.1.6.2.1.1 - Volterra Series Models
Section 2.1.6.2.1.2 - Block Structured Systems
Section 2.1.6.2.1.3 - Neural Network Systems
Section 2.1.6.2.1.4 - NARMAX (Non-Linear Autoregressive Moving Average with Exogenous Inputs) Models
Section 2.1.6.2.1.5 - State-space models (Stochastic Non Linear Models)
Section 2.1.6.3 - Filtering Problem(Stochastic Processes)
Section 2.1.6.3.0 - Basic Writeup - Wikipedia - Filtering Problem (Stochastic Processes)
Section 2.1.6.3.1 - Linear Filters
Section 2.1.6.3.1.0 - Basic Writeup - Wikipedia - Linear Filter
Section 2.1.6.3.1.1 - Kalman Filter
Section 2.1.6.3.1.2 - Weiner Filter
Section 2.6.3.2 - Non-Linear Filters
Section 2.1.6.3.2.0 - Basic Writeup - Wikipedia - Nonlinear Filter
Section 2.1.6.3.2.1 - Extended Kalman Filter
Section 2.1.6.3.3 - Particle Filter
Section 2.1.7 - Statistical Algorithms
Section 2.1.7.0 - Basic Writeup - Wikipedia - Iterative Method
Section 2.1.7.1 - Expectation Maximization Algorithm
Section 2.1.7.1.0 - Basic Writeup - Wikipedia - Expectation Maximimization Algorithm
Section 2.1.7.1.1 - α-EM algorithm
Section 2.1.7.1.2 - Parameter-expanded expectation maximization (PX-EM)
Section 2.1.7.1.3 - Expectation conditional maximization (ECM)
Section 2.1.7.1.4 - Generalized expectation maximization (GEM)
Section 2.1.7.2 - Minorize-Maximization (MM)
Section 2.2.0 - Introductory Writeups
Section 2.2.0.1 - Basic Writeups
Section 2.2.0.1.1 - Part 1 - Wikipedia - Probability
Section 2.2.0.1.2 - Part 2 - Wikipedia - Probability Theory
Section 2.2.0.1.3 - Part 3 - RevisionMath - Revision Math Probability
Section 2.2.0.1.4 - Part 4 - Wikipedia - List of Probability Topics
Section 2.2.0.1.5 - Part 5 - Wikipedia - List of Probability Topics
Section 2.2.0.1.6 - Part 6 - Penn State - Probability Theory and Mathematical Statistics
Section 2.2.0.1.7 - Part 7 - Encyclopedia Britanica - Probability Theory Basic Writeup
Section 2.2.0.1.8 - Part 8 - Encyclopedia Britanica - Probability Theory Basic Writeup
Section 2.2.0.1.9 - Part 9 - Parag Radke - Probability and Statistics
Section 2.2.0.1.10 - Part 10 - Michael Betancourt - Probability Theory (For Scientists and Engineers)
Section 2.2.0.1.11 - Part 11 - Basic Probability and Statistical Concepts
Section 2.2.0.2 - Detailed Writeups
Section 2.2.0.2.1 - Part 1 - Textbook - Grinstead - Introduction to Probability
Section 2.2.0.2.2 - Part 2 - Textbook - Sahoo - Probability and Mathematical Statistics
Section 2.2.0.2.3 - Part 3 - Lecture Notes - Weber - Probability
Section 2.2.0.2.4 - Part 4 - Textbook - Evans,Rosenthal - Probability and Statistics
Section 2.2.0.2.5 - Part 5 - Lecture Notes - Gravner - Introductory Probability
Section 2.2.0.2.6 - Part 6 - Textbook - Ross - A First Course In Probability
Section 2.2.0.2.7 - Part 7 - Review - Maleki,Do - Review of Probability Theory
Section 2.2.0.2.8 - Part 8 - Textbook - DeGroot,Schervish - Probability And Statistics
Section 2.2.0.3 - Examples and Code
Section 2.2.0.3.1 - Part 1 - Textbook with Solved Problems - Schaum - Probability
Section 2.2.0.3.2 - Part 2 - Textbook with Solved Problems - Schaum - Easy Outlines: Probability and Statitics
Section 2.2.0.5.3 - Part 3 - Github - Topic: Probability
Section 2.2.0.5.4 - Part 4 - Cam Davidson Pilon - Probabilistic Programming and Bayesian Methods for Hackers
Section 2.2.0.4 - Videos
Section 2.2.0.4.1 - Part 1 - Khan Academy - Probability
Section 2.2.0.4.2 - Part 2 - MIT - Probabilistic Systems Analysis and Applied Probability
Section 2.2.0.4.3 - Part 3 - MIT - Probabilistic Systems Analysis and Applied Probability
Section 2.2.0.4.4 - Part 4 - MIT OpenCourseWare - Introduction to Probability
Section 2.2.0.4.5 - Part 5 - Khan Academy - Random Variables and Probability Distributions
Section 2.2.0.4.6 - Part 6 - Mathematical Monk - Probability Primer
Section 2.2.1 - Basic Probability
Section 2.2.1.1 - Events
Section 2.2.1.1.0 - Basic Writeup - Wikipedia - Events (Probability Theory)
Section 2.2.1.1.1 - Elementary Events
Section 2.2.1.1.2 - Mutual Exclusivity
Section 2.2.1.1.3 - Impossible event
Section 2.2.1.1.4 - Complementary event
Section 2.2.1.2 - Elementary Probability
Section 2.2.1.2.1 - Axioms of Probability
Section 2.2.1.2.2 - Boole's Inequality
Section 2.2.1.2.3 - Probability Space
Section 2.2.1.2.3.0 - Basic Writeup - Wikipedia - Probability Space
Section 2.2.1.2.3.1 - Sample Space
Section 2.2.1.2.3.2 - Random Element
Section 2.2.1.2.3.3 - Random Compact Set
Section 2.2.1.2.3.4 - Dynkin System
Section 2.2.1.2.3.5 - σ-algebras
Section 2.2.1.2.6 - Probability Measure
Section 2.2.1.2.7 - Credal Set
Section 2.2.1.3 - Meaning of Probability
Section 2.2.1.3.0 - Basic Writeup - Wikipedia - Meaning of Probability
Section 2.2.1.3.1 - Probability interpretations
Section 2.2.1.3.2 - Bayesian Probability
Section 2.2.1.3.3 - Frequency Probability
Section 2.2.1.3.4 - Free Probability
Section 2.2.1.3.5 - Exotic Probability
Section 2.2.1.4 - Calculating with Probability
Section 2.2.1.4.1 - Conditional Probability
Section 2.2.1.4.1.0 - Basic Writeup - Wikipedia - Conditional Probability
Section 2.2.1.4.1.1 - Conditioning (probability)
Section 2.2.1.4.1.2 - Conditional Expectation
Section 2.2.1.4.1.3 - Conditional probability distribution
Section 2.2.1.4.1.4 - Regular conditional probability
Section 2.2.1.4.1.5 - Disintegration theorem
Section 2.2.1.4.1.6 - Bayes' theorem
Section 2.2.1.4.1.7 - Rule of succession
Section 2.2.1.4.1.8 - Conditional independence
Section 2.2.1.4.1.9 - Conditional event algebra
Section 2.2.1.4.1.10 - Goodman–Nguyen–van Fraassen algebra
Section 2.2.1.4.2 - Law of Total Probability
Section 2.2.1.4.3 - Bayes Theorem
Section 2.2.1.5 - Independence
Section 2.2.1.5.0 - Basic Writeup - Wikipedia - Independence
Section 2.2.1.5.1 - Borel-Canteli Lemmas
Section 2.2.1.5.2 - Zero–one law
Section 2.2.1.5.2.0 - Basic Writeup - Wikipedia - Zero-One Law
Section 2.2.1.5.2.1 - Kolmogorov's zero–one law
Section 2.2.1.5.2.2 - Hewitt–Savage zero–one law
Section 2.2.1.6 - Randomness
Section 2.2.1.6.0 - Basic Writeup - Wikipedia - Randomness
Section 2.2.1.6.1 - Random Sequence
Section 2.2.1.6.2 - Pseudorandomness
Section 2.2.1.6.3 - Quasirandomness
Section 2.2.2 - Foundations of Probability Theory
Section 2.2.2.1 - Theories
Section 2.2.2.1.1 - Probability theory
Section 2.2.2.1.2 - Dempster–Shafer theory
Section 2.2.2.1.3 - Possibility theory
Section 2.2.2.1.4 - Almost Surely
Section 2.2.2.2 - Probability space
Section 2.2.2.3 - Probability axioms
Section 2.2.2.4 - Normalizing constant
Section 2.2.2.5 - Mutually exclusive
Section 2.2.2.6 - Boole's inequality
Section 2.2.2.7 - Probability density function
Section 2.2.2.8 - Cumulative distribution function
Section 2.2.2.9 - Laws of Probability Theory
Section 2.2.2.9.1 - Law of total cumulance
Section 2.2.2.9.2 - Law of total expectation
Section 2.2.2.9.3 - Law of total probability
Section 2.2.2.9.4 - Law of total variance
Section 2.2.2.9.5 - Cox's Theorem
Section 2.2.2.9.6 - Girsanov's theorem
Section 2.2.2.9.7 - Law of Truly Large Numbers
Section 2.2.2.9.7.0 - Basic Writeup - Wikipedia - Law of Truly Large Numbers
Section 2.2.2.9.7.1 - Littlewood's Law
Section 2.2.2.9.7.2 - Infinite Monkey Theorem
Section 2.2.2.9.8 - Zero–one law
Section 2.2.2.9.8.0 - Basic Writeup - Wikipedia - Zero-One Law
Section 2.2.2.9.8.1 - Kolmogorov's zero–one law
Section 2.2.2.9.8.2 - Hewitt–Savage zero–one law
Section 2.2.2.9.9 - Power law
Section 2.2.2.9.10 - Anderson's theorem
Section 2.2.2.10 - Bayesianism
Section 2.2.2.11 - Prior Probability (A Priori)
Section 2.2.2.12 - Posterior Probability (A Posteriori)
Section 2.2.2.13 - Paradox in Probability
Section 2.2.2.13.1 - Borel's Paradox
Section 2.2.2.13.2 - Bertrand's Paradox
Section 2.2.2.14 - Coherence
Section 2.2.2.15 - Dutch Book
Section 2.2.2.16 - Algebra of Random Variables
Section 2.2.2.17 - Belief Propogation
Section 2.2.2.18 - Transferable belief model
Section 2.2.3 - Probability Distribution Theory
Section 2.2.3.1 - Probability distribution
Section 2.2.3.1.0 - Basic Writeup - Wikipedia - Probability distribution
Section 2.2.3.1.1 - Prior probability distribution
Section 2.2.3.1.2 - Heavy Tailed distribution
Section 2.2.3.1.3 - Truncated distribution
Section 2.2.3.1.4 - Indecomposable distribution
Section 2.2.3.2 - Probability distribution function
Section 2.2.3.3 - Probability density function
Section 2.2.3.4 - Probability mass function
Section 2.2.3.5 - Cumulative distribution function
Section 2.2.3.6 - Quantile
Section 2.2.3.7 - Moment
Section 2.2.3.7.0 - Basic Writeup - Wikipedia - Moment
Section 2.2.3.7.1 - Moment About the Mean
Section 2.2.3.7.2 - Standardized Moment
Section 2.2.3.7.2.0 - Basic Writeup - Wikipedia - Standardized Moment
Section 2.2.3.7.2.1 - Skewness
Section 2.2.3.7.2.2 - Kurtosis
Section 2.2.3.7.2.3 - Locality
Section 2.2.3.7.3 - Cumulant
Section 2.2.3.7.4 - Factorial Moment
Section 2.2.3.7.5 - Expected Value
Section 2.2.3.7.5.0 - Basic Writeup - Wikipedia - Expected Value
Section 2.2.3.7.5.1 - Law of the Unconscious Statistician
Section 2.2.3.7.6 - Second Moment Method
Section 2.2.3.7.7 - Variance
Section 2.2.3.7.7.0 - Basic Writeup - Wikipedia - Variance
Section 2.2.3.7.7.1 - Coefficient of Variance
Section 2.2.3.7.7.2 - Variance-to-mean ratio
Section 2.2.3.7.8 - Covariance Function
Section 2.2.3.7.9 - An Inequality on Location and Scale Parameters
Section 2.2.3.7.10 - Taylor Expansions for the Moments of Functions of Random Variables
Section 2.2.3.7.11 - Moment Problem
Section 2.2.3.7.11.0 - Basic Writeup - Wikipedia - Moment Problem
Section 2.2.3.7.11.1 - Hamburger moment problem
Section 2.2.3.7.11.1.0 - Basic Writeup - Wikipedia - Hamburger moment problem
Section 2.2.3.7.11.1.1 - Carleman's condition
Section 2.2.3.7.11.2 - Hausdorff moment problem
Section 2.2.3.7.11.3 - Trigonometric moment problem
Section 2.2.3.7.11.4 - Stieltjes moment problem
Section 2.2.3.8 - Distance
Section 2.2.3.8.1 - Total variation distance
Section 2.2.3.8.2 - Hellinger distance
Section 2.2.3.9 - Metrics
Section 2.2.3.9.1 - Wasserstein metric
Section 2.2.3.9.2 - Lévy–Prokhorov metric
Section 2.2.3.9.3 - Lévy metric
Section 2.2.3.10 - Continuity correction
Section 2.2.3.11 - Infinite divisibility
Section 2.2.3.12 - Stability (probability)
Section 2.2.3.13 - Probability bounds analysis
Section 2.2.3.14 - Probability box
Section 2.2.4 - Random Variables
Section 2.2.4.1 - Types of Random Variables
Section 2.2.4.1.1 - Discrete random variable
Section 2.2.4.1.1.0 - Basic Writeup - Wikipedia - Discrete random variable
Section 2.2.4.1.1.1 - Probability mass function
Section 2.2.4.1.1.2 - Constant random variable
Section 2.2.4.1.2 - Continuous random variable
Section 2.2.4.1.2.0 - Basic Writeup - Wikipedia - Continuous random variable
Section 2.2.4.1.2.1 - Probability Density Function
Section 2.2.4.1.3 - Mixed random variable
Section 2.2.4.2 - Multivariate random variable
Section 2.2.4.2.0 - Basic Writeup - Wikipedia - Multivariate random variable
Section 2.2.4.2.1 - Joint probability distribution
Section 2.2.4.2.2 - Marginal distribution
Section 2.2.4.2.3 - Kirkwood approximation
Section 2.2.4.3 - Independent identically-distributed random variables
Section 2.2.4.4 - Expected value
Section 2.2.4.5 - Variance
Section 2.2.4.5.0 - Basic Writeup - Wikipedia - Variance
Section 2.2.4.5.1 - Standard deviation
Section 2.2.4.5.2 - Geometric standard deviation
Section 2.2.4.6 - Statistical independence
Section 2.2.4.6.0 - Basic Writeup - Wikipedia - Statistical independence
Section 2.2.4.6.1 - Conditional independence
Section 2.2.4.6.2 - Pairwise independence
Section 2.2.4.6.3 - Covariance
Section 2.2.4.6.4 - Covariance matrix
Section 2.2.4.6.5 - De Finetti's theorem
Section 2.2.4.7 - Correlation
Section 2.2.4.7.0 - Basic Writeup - Wikipedia - Correlation
Section 2.2.4.7.1 - Uncorrelated
Section 2.2.4.7.2 - Correlation function
Section 2.2.4.7.3 - Canonical correlation
Section 2.2.4.8 - Convergence of random variables
Section 2.2.4.8.0 - Basic Writeup - Wikipedia - Convergence of random variables
Section 2.2.4.8.1 - Weak convergence of measures
Section 2.2.4.8.1.0 - Basic Writeup - Wikipedia - Weak convergence of measures
Section 2.2.4.8.1.1 - Helly–Bray theorem
Section 2.2.4.8.1.2 - Slutsky's theorem
Section 2.2.4.8.2 - Skorokhod's representation theorem
Section 2.2.4.8.3 - Lévy's continuity theorem
Section 2.2.4.8.4 - Uniform integrability
Section 2.2.4.9 - Inequalities
Section 2.2.4.9.1 - Jensen's inequality
Section 2.2.4.9.2 - Markov's inequality
Section 2.2.4.9.3 - Chebyshev's inequality
Section 2.2.4.9.4 - Chernoff bound
Section 2.2.4.9.5 - Bernstein inequalities (probability theory)
Section 2.2.4.9.6 - Hoeffding's inequality
Section 2.2.4.9.7 - Kolmogorov's inequality
Section 2.2.4.9.8 - Etemadi's inequality
Section 2.2.4.9.9 - Chung–Erdős inequality
Section 2.2.4.9.10 - Khintchine inequality
Section 2.2.4.9.11 - Paley–Zygmund inequality
Section 2.2.4.10 - Laws of large numbers
Section 2.2.4.10.0 - Basic Writeup - Wikipedia - Laws of large numbers
Section 2.2.4.10.1 - Asymptotic equipartition property
Section 2.2.4.10.2 - Typical set
Section 2.2.4.10.3 - Law of large numbers
Section 2.2.4.10.4 - Kolmogorov's two-series theorem
Section 2.2.4.11 - Random field
Section 2.2.4.11.0 - Basic Writeup - Wikipedia - Random field
Section 2.2.4.11.1 - Conditional Random field
Section 2.2.4.12 - Borel–Cantelli lemma
Section 2.2.4.13 - Wick product
Section 2.2.5 - Probability Distributions
Section 2.2.5.0 - Introductory Writeups
Section 2.2.5.0,1 - Basic Writeup - Wikipedia - Probability Distribution
Section 2.2.5.0.2 - Detailed Writeup - Wikipedia - List of Probability Distributions
Section 2.2.5.1 - Probability Distribution Grouped By Type of Process
Section 2.2.5.1.1 - Bernouli Process based (Yes/No with probability)
Section 2.2.5.1.2 - Categorical outcomes (events with K possible outcomes, with a given probability for each outcome)
Section 2.2.5.1.3 - Related to events in a Poisson process (events that occur independently with a given rate)
Section 2.2.5.1.4 - Real-valued quantities that grow linearly (e.g. errors, offsets)
Section 2.2.5.1.5 - Real-valued quantities that grow exponentially ( e.g. prices, incomes, populations )
Section 2.2.5.1.6 - Real-valued quantities that are assumed to be uniformly distributed over a (possibly unknown) region
Section 2.2.5.1.7 - Real-valued quantities that grow or decrease asymptotically within limits
Section 2.2.5.1.8 - Absolute positive real values of vectors with normally distributed components
Section 2.2.5.1.9 - Normally distributed real quantities operated with sum of squares (for hypothesis testing)
Section 2.2.5.1.10 - Useful as conjugate prior distributions in Bayesian inference
Section 2.2.5.2 - Probability Distribution Grouped By Outcomes
Section 2.2.5.2.1 - Discrete Distributions
Section 2.2.5.2.1.0 - Basic Writeup - Wikipedia - Discrete Probability Distributions
Section 2.2.5.2.1.1 - With Finite Support
Section 2.2.5.2.1.2 - With Infinite Support
Section 2.2.5.2.2 - Continuous Distributions
Section 2.2.5.2.2.0 - Basic Writeup - Wikipedia - Continuous Probability Distributions
Section 2.2.5.2.2.1 - Supported on Bounded Interval
Section 2.2.5.2.2.2 - Supported on intervals of length 2π – directional distributions
Section 2.2.5.2.2.3 - Supported on semi-infinite intervals, usually [0,∞)
Section 2.2.5.2.2.4 - Supported on whole real line
Section 2.2.5.2.2.5 - With Variable Support
Section 2.2.5.2.3 - Mixed Distributions
Section 2.2.5.2.4 - Joint Distributions
Section 2.2.5.2.4.1 - Two or more random variables on the same sample space
Section 2.2.5.2.4.2 - Distributions of matrix-valued random variables
Section 2.2.5.2.5 - Non-Numeric Distributions
Section 2.2.5.2.6 - Symmetric Distributions
Section 2.2.5.2.6.0 - Basic Writeup - Wikipedia - Symmetric Probability Distribution
Section 2.2.5.2.6.1 - List of Symmetric Distributions
Section 2.2.5.2.7 - Miscellaneous Distributions
Section 2.2.6 - Properties of Probability Distributions
Section 2.2.6.1 - General Theorems
Section 2.2.6.1.1 - Central limit theorem
Section 2.2.6.1.1.0 - Basic Writeup - Wikipedia - Central limit theorem
Section 2.2.6.1.1.1 - Illustration of the central limit theorem
Section 2.2.6.1.1.2 - Concrete illustration of the central limit theorem
Section 2.2.6.1.1.3 - Berry–Esséen theorem
Section 2.2.6.1.1.4 - De Moivre–Laplace theorem
Section 2.2.6.1.1.5 - Lyapunov's central limit theorem
Section 2.2.6.1.1.6 - Martingale central limit theorem
Section 2.2.6.1.1.7 - Infinite divisibility (probability)
Section 2.2.6.1.1.8 - Method of moments (probability theory)
Section 2.2.6.1.1.9 - Stability (probability)
Section 2.2.6.1.1.10 - Stein's lemma
Section 2.2.6.1.2 - Helly–Bray theorem
Section 2.2.6.1.3 - Maxwell's theorem
Section 2.2.6.1.4 - Le Cam's theorem
Section 2.2.6.2 - Characteristic function (probability theory)
Section 2.2.6.2.0 - Basic Writeup - Wikipedia - Characteristic function (probability theory)
Section 2.2.6.2.1 - Lévy continuity theorem
Section 2.2.6.3 - Edgeworth series
Section 2.2.6.4 - Location parameter
Section 2.2.6.5 - Moment-generating function
Section 2.2.6.5.0 - Basic Writeup - Wikipedia - Moment-generating function
Section 2.2.6.5.1 - Factorial moment generating function
Section 2.2.6.6 - Negative probability
Section 2.2.6.7 - Probability-generating function
Section 2.2.6.8 - Vysochanskiï–Petunin inequality
Section 2.2.6.9 - Mutual information
Section 2.2.6.10 - Kullback–Leibler divergence
Section 2.2.6.11 - Normally distributed and uncorrelated does not imply independent
Section 2.2.6.12 - Large deviations theory
Section 2.2.6.12.0 - Basic Writeup - Large deviations theory
Section 2.2.6.12.1 - Contraction principle (large deviations theory)
Section 2.2.6.12.2 - Varadhan's lemma
Section 2.2.6.12.3 - Tilted large deviation principle
Section 2.2.6.12.4 - Rate function
Section 2.2.6.12.5 - Laplace principle (large deviations theory)
Section 2.2.6.12.6 - Exponentially equivalent measures
Section 2.2.6.12.7 - Cramér's theorem (large deviations)
Section 2.2.7 - Generating Functions
Section 2.2.7.1 - Probability-generating functions
Section 2.2.7.2 - Moment-generating functions
Section 2.2.7.3 - Laplace transforms
Section 2.2.7.4 - Laplace–Stieltjes transforms
Section 2.2.7.5 - Characteristic functions
Section 2.2.8 - Convergence of Random Variables
Section 2.2.8.0 - Basic Writeup - Wikipedia - Convergence in Random Variables
Section 2.2.8.1 - Convergence in distribution
Section 2.2.8.2 - Convergence in probability
Section 2.2.8.3 - Almost sure convergence
Section 2.2.8.4 - Skorokhod's representation theorem
Section 2.2.9 - Stochastic Processes
Section 2.2.9.0 - Basic Writeup - Wikipedia - Stochastic Processes and Basic Definitions
Section 2.2.9.1 - Common Stochastic Processes
Section 2.2.9.1.1 - Chinese restaurant process
Section 2.2.9.1.2 - Adapted process
Section 2.2.9.1.3 - Point process
Section 2.2.9.1.4 - Branching process
Section 2.2.9.1.5 - Bernoulli process
Section 2.2.9.1.5.0 - Basic Writeup - Wikipedia - Bernoulli process
Section 2.2.9.1.5.1 - Bernoulli Scheme
Section 2.2.9.1.6 - Random walk
Section 2.2.9.1.6.0 - Basic Writeup - Wikipedia - Random walk
Section 2.2.9.1.6.1 - Random walk Monte Carlo
Section 2.2.9.1.6.2 - Loop-erased random walk
Section 2.2.9.1.6.3 - Law of the iterated logarithm
Section 2.2.9.1.7 - Poisson process
Section 2.2.9.1.7.0 - Basic Writeup - Wikipedia - Poisson process
Section 2.2.9.1.7.1 - Compound Poisson process
Section 2.2.9.1.7.2 - Poisson random measure
Section 2.2.9.1.7.3 - Renewal theory
Section 2.2.9.1.8 - Wiener process
Section 2.2.9.1.8.0 - Basic Writeup - Wikipedia - Wiener process
Section 2.2.9.1.8.1 - Brownian motion
Section 2.2.9.1.8.2 - Brownian motion
Section 2.2.9.1.8.3 - Geometric Brownian motion
Section 2.2.9.1.8.4 - Donsker's theorem
Section 2.2.9.1.8.5 - Empirical process
Section 2.2.9.1.8.6 - Wiener equation
Section 2.2.9.1.8.7 - Wiener Sausage
Section 2.2.9.1.9 - Brownian Process (Motion)
Section 2.2.9.1.9.0 - Basic Writeup - Wikipedia - Brownian Process (Motion)
Section 2.2.9.1.9.1 - Geometric Brownian motion
Section 2.2.9.1.9.2 - Fractional Brownian motion
Section 2.2.9.1.9.3 - Brownian bridge
Section 2.2.9.1.10 - Ornstein–Uhlenbeck process
Section 2.2.9.1.11 - Gamma process
Section 2.2.9.1.12 - Gaussian process
Section 2.2.9.1.12.0 - Basic Writeup - Wikipedia - Gaussian process
Section 2.2.9.1.12.1 - Gaussian random field
Section 2.2.9.1.12.2 - Gaussian isoperimetric inequality
Section 2.2.9.1.12.3 - Large deviations of Gaussian random functions
Section 2.2.9.1.13 - Increasing process
Section 2.2.9.1.14 - Markov process
Section 2.2.9.1.14.0 - Basic Writeups
Section 2.2.9.1.14.0.1 - Part 1 - Wikipedia - Markov process
Section 2.2.9.1.14.0.2 - Part 2 - Wikipedia - Markov process (By Category)
Section 2.2.9.1.14.1 - Markov Chain
Section 2.2.9.1.14.1.0 Basic Writeup - Wikipedia - Markov Chain
Section 2.2.9.1.14.1.1 Examples of Markov chains
Section 2.2.9.1.14.1.2 Detailed balance
Section 2.2.9.1.14.1.3 Detailed balance
Section 2.2.9.1.14.1.4 - Markov property
Section 2.2.9.1.14.1.5 - Hidden Markov model
Section 2.2.9.1.14.1.6 - Maximum-entropy Markov model
Section 2.2.9.1.14.1.7 - Markov chain mixing time
Section 2.2.9.1.14.1.8 - Population processes
Section 2.2.9.1.14.2 - Markov Partition
Section 2.2.9.1.14.3 - Continuous-time Markov process
Section 2.2.9.1.14.4 - Piecewise-deterministic Markov process
Section 2.2.9.1.14.5 - Chapman–Kolmogorov equation
Section 2.2.9.1.14.6 - Chapman–Kolmogorov equation
Section 2.2.9.1.15 - Branching process
Section 2.2.9.1.15.0 - Basic Writeup - Branching process
Section 2.2.9.1.15.1 - Galton–Watson process
Section 2.2.9.1.16 - Gauss–Markov process
Section 2.2.9.1.17 - Stationary process
Section 2.2.9.1.18 - Lévy process
Section 2.2.9.1.19 - Voter model
Section 2.2.9.2 - Martingale
Section 2.2.9.2.0 - Basic Writeup - Wikipedia - Martingale
Section 2.2.9.2.1 - Doob martingale
Section 2.2.9.2.2 - Optional stopping theorem
Section 2.2.9.2.3 - Martingale representation theorem
Section 2.2.9.2.4 - Azuma's inequality
Section 2.2.9.2.5 - Wald's equation
Section 2.2.9.4 - Time Series Analysis
Section 2.2.9.4.0 - Basic Writeup - Wikipedia - Time Series Analysis
Section 2.2.9.4.1 - Moving-average
Section 2.2.9.4.2 - Autoregressive Model
Section 2.2.9.4.3 - Autoregressive Moving Average Model
Section 2.2.9.4.4 - Autoregressive integrated moving average model
Section 2.2.9.4.5 - Anomaly Time Series
Section 2.2.9.4.6 - Correlation Function
Section 2.2.9.4.7 - Autocorrelation Function
Section 2.2.9.5 - Stochastic Differential Equations
Section 2.2.9.5.1 - Stochastic calculus
Section 2.2.9.5.1.0 - Basic Writeup - Wikipedia - Stochastic calculus
Section 2.2.9.5.1.1 - Itô calculus
Section 2.2.9.5.1.2 - Malliavin calculus
Section 2.2.9.5.1.3 - Stratonovich integral
Section 2.2.9.5.2 - Diffusions
Section 2.2.9.5.2.0 - Basic Writeup - Wikipedia - Diffusions
Section 2.2.9.5.2.1 - Jump diffusion
Section 2.2.9.5.2.2 - Basic Affine Jump diffusion
Section 2.2.9.5.2.3 - Brownian Motion
Section 2.2.9.5.2.4 - Wiener process
Section 2.3.0 - Introductory Writeups
Section 2.3.0.1 - Basic Writeups
Section 2.3.0.1.1 - Part 1 - Katariya - Introduction to Algebra
Section 2.3.0.1.2 - Part 2 - Wikipedia - List of Linear Algebra topics
Section 2.3.0.1.3 - Part 3 - Wikipedia - Matrices
Section 2.3.0.1.3 - Part 4 - Wikipedia - List of Matrices
Section 2.3.0.1.5 - Part 5 - DeepLearningOrg - Linear Algebra for Deep Learning
Section 2.3.0.1.6 - Part 6 - Wikibooks - Linear Algebra
Section 2.3.0.1.7 - Part 7 - Robert A Beezer - A first course in Linear Algebra
Section 2.3.0.1.8 - Part 8 - Wikipedia - Algebra Portal
Section 2.3.0.2 - Detailed Writeups
Section 2.3.0.2.1 - Part 1 - Cherney,Denton,Thomas,Waldron - Linear Algebra
Section 2.3.0.2.2 - Part 2 - Dawkins - Linear Algebra
Section 2.3.0.2.3 - Part 3 - Carrell - Fundamentals of Linear Algebra
Section 2.3.0.2.4 - Part 4 - Lipschutz-Lipson - Schaum's Linear Algebra
Section 2.3.0.2.5 - Part 5 - Lang - Introduction to Linear Algebra
Section 2.3.0.2.6 - Part 6 - Strang 4rth Edition - Linear Algebra and its applications
Section 2.3.0.2.7 - Part 7 - Hoffman,Kunze - Linear Algebra
Section 2.3.0.3 - Videos
Section 2.3.0.3.1 - Part 1 - 3Blue1Brown - Essence of Linear Algebra
Section 2.3.0.3.2 - Part 2 - MIT - Gilbert Linear Albegra Course by Gilbert Strang
Section 2.3.0.3.3 - Part 3 - Imperial College London - Linear Albegra for Machine Learning
Section 2.3.0.3.4 - Part 4 - Imperial College London - Linear Albegra for Machine Learning
Section 2.3.0.3.5 - Part 5 - Khan Academy - Linear Algebra
Section 2.3.0.3.6 - Part 6 - Khan Academy - Linear Algebra
Section 2.3.0.3.7 - Part 7 - Racheal Thomas - Computational Linear Algebra
Section 2.3.1 - Basic Concepts
Section 2.3.1.1 - Numerical Linear Algebra
Section 2.3.1.2 - Fundamental Theorem of Algebra
Section 2.3.1.3 - Fundamental Theorem of Linear Algebra
Section 2.3.1.4 - Scalar
Section 2.3.1.5 - Scalar Multiplication
Section 2.3.1.6 - Vector Space
Section 2.3.1.7 - Vector Projection
Section 2.3.1.8 - Linear Map
Section 2.3.1.9 - Linear Projection
Section 2.3.1.10 - Basis
Section 2.3.1.11 - Change of Basis
Section 2.3.1.12 - Matrices
Section 2.3.1.13 - Row And Column Space
Section 2.3.1.14 - Orthogonality
Section 2.3.1.15 - Determinant
Section 2.3.1.16 - Eigenvalues and Eigenvectors
Section 2.3.1.17 - Duality
Section 2.3.1.17.0 - Basic Writeup - Wikipedia - Duality
Section 2.3.1.17.1 - Dual Map
Section 2.3.1.17.2 - Inner Product Space
Section 2.3.1.18 - Linear Algebra Machine Learning Examples
Section 2.3.1.18.1 - Linear Regression
Section 2.3.1.18.2 - Regularization
Section 2.3.1.18.3 - Principal Component Analysis
Section 2.3.1.18.4 - One Hot Encoding
Section 2.3.1.18.5 - Latent Semantic Analysis
Section 2.3.1.18.6 - Recommender System
Section 2.3.1.18.7 - Deep Learning
Section 2.3.2 - Vectors and Vector spaces
Section 2.3.2.0 - Basic Writeup - Wikipedia - Vector
Section 2.3.2.1 - Vector Algebra
Section 2.3.2.1.0 - Basic Writeup - UNL - Vector Algebra
Section 2.3.2.1.1 - Scalar multiplication
Section 2.3.2.1.2 - Vector Dot Product
Section 2.3.2.1.3 - Vector Dot Product
Section 2.3.2.1.4 - Bilinear Map
Section 2.3.2.1.4.0 - Basic Writeup - Wikipedia - Bilinear Map
Section 2.3.2.1.4.1 - Cross product
Section 2.3.2.1.4.2 - Triple product
Section 2.3.2.1.4.3 - Seven-dimensional Cross Product
Section 2.3.2.2 - Specific Vector Types
Section 2.3.2.2.1 - Zero Vector
Section 2.3.2.2.2 - Basis Vector
Section 2.3.2.2.3 - Unit Vector
Section 2.3.2.2.4 - Isotropic(Null) Vector
Section 2.3.2.2.5 - Column Vector
Section 2.3.2.2.6 - Row and Column Vector
Section 2.3.2.2.7 - Coordinate Vector
Section 2.3.2.2.8 - PseudoVector
Section 2.3.2.2.9 - Tangent Vector
Section 2.3.2.2.10 - Normal Vector
Section 2.3.2.2.11 - Gradient Vector
Section 2.3.2.2.12 - More Categories of Vectors
Section 2.3.2.3 - Vector Norms
Section 2.3.2.3.0 - Basic Writeup - Wikipedia - Vector Norms
Section 2.3.2.3.1 - Distance Metrics
Section 2.3.2.3.1.1 - Euclidean (Pythagorean) Distance
Section 2.3.2.3.1.2 - Chebyshev Distance
Section 2.3.2.3.1.3 - Manhattan (Rectilinear,L1,Snake,City Block) Distance
Section 2.3.2.3.1.4 - Minkowski Distance
Section 2.3.2.3.1.5 - Haversine Distance
Section 2.3.2.3.2 - Vector L1 Norm (Taxicab Metric - Taxicab Geometry)
Section 2.3.2.3.3 - Vector L2 (Euclidean) Norm
Section 2.3.2.3.1.4 - Vector Max(Infinity/Uniform/Supremum) Norm
Section 2.3.2.4 - Vector Products
Section 2.3.2.4.1 - Outer Product
Section 2.3.2.4.2 - Inner Product Space
Section 2.3.2.4.3 - Dot Product
Section 2.3.2.4.4 - Cross Product
Section 2.3.2.4.5 - Direct Product
Section 2.3.2.4.6 - Triple Product (Scalar and Vector)
Section 2.3.2.5 - Vector Space
Section 2.3.2.5.0 - Basic Writeups
Section 2.3.2.5.0.1 - Part 1 - Wikipedia - Vector Space
Section 2.3.2.5.0.2 - Part 2 - Wikibooks - Definitions and Examples
Section 2.3.2.5.0.3 - Part 3 - Wikipedia - More Examples of Vector Spaces
Section 2.3.2.5.0.4 - Part 4 - Wikipedia - Categories of Vector Spaces
Section 2.3.2.5.1 - Subspace and Spanning Sets
Section 2.3.2.5.2 - Dual Space
Section 2.3.2.5.2.0 - Basic Writeup - Wikipedia - Dual Space
Section 2.3.2.5.2.1 - Linear Function
Section 2.3.2.5.2.2 - Linear Functional
Section 2.3.2.5.2.3 - Algebraic Dual Space
Section 2.3.2.5.2.4 - Continuous Dual Space
Section 2.3.2.5.3 - Linear Subspace
Section 2.3.2.5.3.0 - Basic Writeup - Wikipedia - Linear Subspace
Section 2.3.2.5.3.1 - Row and Column Spaces
Section 2.3.2.5.3.2 - Cyclic Subspace
Section 2.3.2.5.3.3 - Null(Kernel) Space
Section 2.3.2.5.4 - Linear Span
Section 2.3.2.5.5 - Basis (Linear Algebra)
Section 2.3.2.5.6 - Quotient Vector Space
Section 2.3.2.5.7 - Normed Vector Space
Section 2.3.2.5.8 - Graded Vector Space
Section 2.3.2.5.9 - Ordered Vector Space
Section 2.3.2.5.10 - Super Vector Space
Section 2.3.2.5.11 - Topological Vector Space
Section 2.3.2.5.11.0 - Basic Writeup - Wikipedia - Topololigical Vector Space
Section 2.3.2.5.11.1 - F-Spaces
Section 2.3.2.5.11.2 - Locally Convex
Section 2.3.2.5.11.2.0 - Basic Writeup - Wikipedia - Locally Convex
Section 2.3.2.5.11.2.1 - Barrelled Spaces
Section 2.3.2.5.11.2.1.0 - Basic Writeup - Wikipedia - Barrelled Spaces
Section 2.3.2.5.11.2.1.1 - Montel Space
Section 2.3.2.5.11.2.2 - Bornological Spaces
Section 2.3.2.5.11.2.3 - Stereotype Space
Section 2.3.2.5.11.2.4 - Fréchet spaces
Section 2.3.2.5.11.2.4.0 - Basic Writeup - Wikipedia - Fréchet spaces
Section 2.3.2.5.11.2.4.1 - Fréchet Algebra
Section 2.3.2.5.11.2.4.2 - LF-spaces
Section 2.3.2.5.11.2.5 - Nuclear spaces
Section 2.3.2.5.11.2.6 - Normed Spaces
Section 2.3.2.5.11.2.6.0 - Basic Writeup - Wikipedia - Normed Spaces
Section 2.3.2.5.11.2.6.1 - Banach Spaces
Section 2.3.2.5.11.2.6.1.0 - Basic Writeup - Wikipedia - Banach Spaces
Section 2.3.2.5.11.2.6.1.1 - Banach Algebra
Section 2.3.2.5.11.2.6.1.1.0 - Basic Writeup - Wikipedia - Banach Algebra
Section 2.3.2.5.11.2.6.1.1.1 - C*-Algebra
Section 2.3.2.5.11.2.6.1.1.1.0 - Basic Writeup - Wikipedia - C*-Algebra
Section 2.3.2.5.11.2.6.1.1.1.1 - Von Neumann Algebra
Section 2.3.2.5.11.2.6.2 - Hardy paces
Section 2.3.2.5.11.2.6.3 - Hilbert Spaces
Section 2.3.2.5.11.2.7 - Semi-Normed Spaces
Section 2.3.2.5.11.2.8 - Sobolov Spaces
Section 2.3.2.5.12 - Symplectic Vector Space
Section 2.3.2.5.13 - Algebra Over Fields
Section 2.3.2.5.14 - Lie Algebra
Section 2.3.2.5.15 - Dimension Theorem For Vector Spaces
Section 2.3.2.5.15.0 - Basic Writeup - Wikipedia - Dimension Theorem For Vector Spaces
Section 2.3.2.5.15.1 - Hamel Dimension
Section 2.3.2.6 - Maps Between Spaces
Section 2.3.2.6.1 - Linear map (transformation, linear function)
Section 2.3.2.6.1.0 - Basic Writeup - Wikipedia - Linear map (transformation, linear function)
Section 2.3.2.6.1.1 - Geometry of Linear Maps
Section 2.3.2.6.1.2 - The Matrix of a Linear Map
Section 2.3.2.6.1.3 - Discontinuous Linear Maps
Section 2.3.2.6.1.4 - Projections of Linear Maps
Section 2.3.2.6.1.4.0 - Basic Writeup - Wikipedia - Projections of Linear Maps
Section 2.3.2.6.1.4.1 - Projection Onto a Subspace
Section 2.3.2.6.1.4.2 - Vector Projection
Section 2.3.2.6.1.4.2.0 - Basic Writeup - Wikipedia - Vector Projection
Section 2.3.2.6.1.4.2.1 - Orthogonal Projection
Section 2.3.2.6.1.4.2.2 - Orthogonal Projection Onto a Line
Section 2.3.2.6.1.4.2.3 - Parallel Projection
Section 2.3.2.6.1.4.3 - Gram-Schmidt Orthogonalization
Section 2.3.2.6.2 - Shear mapping or Galilean transformation
Section 2.3.2.6.3 - Squeeze mapping or Lorentz transformation
Section 2.3.2.6.4 - Tranformation Matrix
Section 2.3.2.6.6 - Kernel
Section 2.3.2.6.7 - Cokernel
Section 2.3.2.6.8 - Algebraic Classifications
Section 2.3.2.6.8.1 - Epimorphism (Surjective)
Section 2.3.2.6.8.2 - Isomorphism
Section 2.3.2.6.8.2.0 - Basic Definition - Wikipedia - Isomorphism
Section 2.3.2.6.8.2.1 - Definition and Examples
Section 2.3.2.6.8.2.2 - Dimension Characterizes Isomorphism
Section 2.3.2.6.8.3 - Endomorphism
Section 2.3.2.6.8.3.0 - Basic Writeup - Wikipedia - Endomorphism
Section 2.3.2.6.8.3.1 - Eigenvalue, eigenvector and eigenspace
Section 2.3.2.6.8.3.1.0 - Basic Writeup - Wikipedia - Eigenvalue, eigenvector and eigenspace
Section 2.3.2.6.8.3.1.1 - Cayley–Hamilton theorem
Section 2.3.2.6.8.3.1.2 - Spread of a matrix
Section 2.3.2.6.8.3.1.3 - Jordan normal form
Section 2.3.2.6.8.3.1.4 - Weyr canonical form
Section 2.3.2.6.8.3.1.5 - Eigenvectors from Eigenvalues
Section 2.3.2.6.8.4 - Homomorphisms
Section 2.3.2.6.8.4.0 - Basic Writeup - Wikipedia - Homomorphisms
Section 2.3.2.6.8.4.1 - Rangespace and Nullspace
Section 2.3.2.6.8.4.2 - Monomorphism (Injective homomorphism)
Section 2.3.2.6.9 - Computing Linear Maps
Section 2.3.2.6.9.0 - Basic Writeup - Wikipedia - Computing Linear Maps
Section 2.3.2.6.9.1 - Representing Linear Maps with Matrices
Section 2.3.2.6.9.2 - Any Matrix Represents a Linear Map
Section 2.3.2.6.10 - Basis
Section 2.3.2.6.10.0 - Basic Writeup - Wikipedia - Basis
Section 2.3.2.6.10.1 - Subspaces
Section 2.3.2.6.10.2 - Quotient Spaces
Section 2.3.2.6.10.3 - Direct product
Section 2.3.2.6.10.4 - Direct Sum (Of Groups)
Section 2.3.2.6.10.5 - Tensor Product
Section 2.3.2.6.10.6 - Change of Basis
Section 2.3.2.6.10.6.0 - Basic Writeup - Wikipedia - Change of Basis
Section 2.3.2.6.10.6.1 - Changing Representations of Vectors
Section 2.3.2.6.10.6.2 - Changing Map Representations
Section 2.3.2.6.10.7 - Hamel Basis
Section 2.3.2.6.11 - Line of Best Fit
Section 2.3.2.6.12 - Markov Chains
Section 2.3.2.6.13 - Orthonormal Matrices
Section 2.3.3 - Systems of Linear Equations
Section 2.3.3.0 - Basic Writeup - Wikipedia - Systems of Linear Equations
Section 2.3.3.1 - Linear Equations
Section 2.3.3.1.0 - Basic Writeup - Wikipedia - Linear Equations
Section 2.3.3.1.1 - Determinant
Section 2.3.3.1.2 - Minor(Linear Algebra)
Section 2.3.3.1.3 - Cauchy–Binet formula
Section 2.3.3.1.4 - Cramer's rule
Section 2.3.3.1.5 - Gaussian(Gauss-Jordan) Elimination
Section 2.3.3.1.6 - Strassen algorithm
Section 2.3.3.2 - Solving Linear Systems of Equations (See Section 2.3.10.2 for detailed breakdown in Numerical Linear Algebra)
Section 2.3.3.3 - Linear Geometry of n-Space
Section 2.3.3.3.0 - Basic Writeup - Wikibooks - Linear Geometry of n-Space
Section 2.3.3.3.1 - Vectors in Space
Section 2.3.3.3.2 - Length and Angle Measures
Section 2.3.3.4 - Reduced Echelon Form
Section 2.3.3.4.0 - Basic Writeup - Wikibooks - Reduced Echelon Form
Section 2.3.3.4.1 - Gauss-Jordan Reduction
Section 2.3.3.4.2 - Row Equivalence
Section 2.3.3.5 - Computer Algebra Systems
Section 2.3.3.6 - Input-Output Analysis
Section 2.3.3.7 - Accuracy of Computations
Section 2.3.3.8 - Analyzing Networks
Section 2.3.3.9 - Speed of Gauss' Method
Section 2.3.3.10 - Linear span
Section 2.3.3.11 - Linear independence
Section 2.3.3.12 - Linear combination
Section 2.3.4 - Similarity
Section 2.3.4.0 - Basic Writeup - Wikibooks - Similarity
Section 2.3.4.1 - Definition and Examples
Section 2.3.4.2 - Diagonalizability
Section 2.3.4.3 - Eigenvalues and Eigenvectors
Section 2.3.4.4 - Complex Vector Spaces
Section 2.3.4.4.0 - Basic Writeup - Wikibooks - Complex Vector Spaces
Section 2.3.4.4.1 - Factoring and Complex Numbers: A Review
Section 2.3.4.4.2 - Complex Representations
Section 2.3.4.5 - Nilpotence
Section 2.3.4.5.0 - Basic Writeup - Wikibooks - Nilpotence
Section 2.3.4.5.1 - Self-Composition
Section 2.3.4.5.2 - Strings
Section 2.3.4.6 - Jordan Form
Section 2.3.4.6.0 - Basic Writeup - Wikibooks - Jordan Form
Section 2.3.4.6.1 - Polynomials of Maps and Matrices
Section 2.3.4.6.2 - Jordan Canonical Form
Section 2.3.4.7 - Geometry of Eigenvalues
Section 2.3.4.8 - The Method of Powers
Section 2.3.4.9 - Stable Populations
Section 2.3.4.10 - Linear Recurrences
Section 2.3.5 - Matrices
Section 2.3.5.0 - Basic Writeup - Wikipedia - Matrices
Section 2.3.5.1 - Matrix Operations
Section 2.3.5.1.1 - Matrix addition
Section 2.3.5.1.2 - Matrix multiplication
Section 2.3.5.1.2.0 - Basic Writeup - Wikipedia - Matrix multiplication
Section 2.3.5.1.2.1 - Mechanics of Matrix Multiplication
Section 2.3.5.1.2.2 - Algorithms for matrix multiplication:
Section 2.3.5.1.2.2.1 - Strassen algorithm
Section 2.3.5.1.2.2.2 - Coppersmith–Winograd algorithm
Section 2.3.5.1.2.2.3 - Cannon's algorithm
Section 2.3.5.1.2.2.4 - Freivalds' algorithm
Section 2.3.5.1.3 - Matrix Norms
Section 2.3.5.1.4 - Matrix Splitting
Section 2.3.5.1.5 - Basis transformation matrix
Section 2.3.5.1.6 - Sums and Scalar Products
Section 2.3.5.1.7 - Invertable Matrix
Section 2.3.5.1.8 - Pseudoinverse
Section 2.3.5.1.9 - Transpose
Section 2.3.5.1.9.0 - Basic Writeup - Wikipedia - Transpose
Section 2.3.5.1.9.1 - Symmetric matrix ( A = AT )
Section 2.3.5.1.9.2 - Orthogonal matrix ( AT = A-1 )
Section 2.3.5.1.9.3 - Skew-symmetric matrix ( AT = -A )
Section 2.3.5.1.9.4 - Conjugate Transpose matrix
Section 2.3.5.1.9.4.0 - Basic Writeup - Wikipedia - Conjugate Transpose matrix
Section 2.3.5.1.9.4.1 - Unitary matrix
Section 2.3.5.1.9.4.2 - Hermitian matrix
Section 2.3.5.1.9.4.3 - Skew-Hermitian (Antihermitian) matrix
Section 2.3.5.1.10 - Rank
Section 2.3.5.1.11 - Square Matrix
Section 2.3.5.1.11.0 - Basic Writeup - Wikipedia - Square Matrix
Section 2.3.5.1.11.1 - Trace
Section 2.3.5.1.11.2 - Determinant
Section 2.3.5.1.11.2.0 - Basic Writeup - Wikipedia - Determinant
Section 2.3.5.1.11.2.1 - Determinants as Size Functions
Section 2.3.5.1.11.2.2 - Laplace's Expansion
Section 2.3.5.1.11.2.3 - Cramer's Rule
Section 2.3.5.1.11.2.4 - Speed of Calculating Determinants
Section 2.3.5.1.11.2.5 - Projective Geometry
Section 2.3.5.1.11.3 - Characteristic polynomial
Section 2.3.5.1.11.4 - Cofactor
Section 2.3.5.1.11.5 - Adjugate
Section 2.3.5.1.11.6 - Pfaffian
Section 2.3.5.1.11.7 - Minor
Section 2.3.5.2 - Row and column spaces
Section 2.3.5.3 - Spectral theorem
Section 2.3.5.4 - Perron–Frobenius theorem
Section 2.3.5.5 - Types of Matrix
Section 2.3.5.5.1 - Square Matrix and Types
Section 2.3.5.5.1.0 - Basic Writeup - Wikipedia - Square Matrix
Section 2.3.5.5.1.1 - Diagonal Matrix
Section 2.3.5.5.1.2 - Triangular Matrix
Section 2.3.5.5.1.3 - Identity Matrix
Section 2.3.5.5.1.4 - Orthogonal Matrix
Section 2.3.5.5.1.5 - Symmetric Matrix
Section 2.3.5.5.1.5.0 - Basic Writeup - Wikipedia - Symmetric Matrix
Section 2.3.5.5.1.5.1 - Hessian Matrix
Section 2.3.5.5.1.5.2 - Antimetric Matrix
Section 2.3.5.5.1.5.3 - Centrosymmetric Matrix
Section 2.3.5.5.1.5.4 - Circulant Matrix
Section 2.3.5.5.1.5.5 - Covariance Matrix
Section 2.3.5.5.1.5.6 - Coxeter Matrix
Section 2.3.5.5.1.5.7 - Hankel Matrix
Section 2.3.5.5.1.5.8 - Hilbert Matrix
Section 2.3.5.5.1.5.9 - Persymmetric Matrix
Section 2.3.5.5.1.5.10 - Skew-symmetric Matrix
Section 2.3.5.5.1.5.11 - Toeplitz Matrix
Section 2.3.5.5.1.5.12 - Hessenberg Matrix
Section 2.3.5.5.1.5.13 - Stochastic Matrix
Section 2.3.5.5.1.5.14 - Hankel Matrix
Section 2.3.5.5.1.6 - Unitary Matrix
Section 2.3.5.5.1.7 - Hermitian Matrix
Section 2.3.5.5.1.8 - Skew(Anti) Hermitian Matrix
Section 2.3.5.5.1.9 - Positive-definite and Semi-Definite Matrix
Section 2.3.5.5.2 - Band Matrix
Section 2.3.5.5.2.0 - Basic Writeup - Wikipedia - Band Matrix
Section 2.3.5.5.2.1 - Tridiagonal Matrix
Section 2.3.5.5.3 - Block Matrix
Section 2.3.5.5.4 - Sparse Matrix
Section 2.3.5.5.5 - Vandermonde Matrix
Section 2.3.5.5.6 - Logical (0,1) Matrix
Section 2.3.5.5.7 - Sparse Matrix
Section 2.3.5.6 - Some useful matrix identities
Section 2.3.5.6.1 - Matrix-vector product as linear combination of matrix columns
Section 2.3.5.6.2 - Sum of outer products as matrix-matrix product
Section 2.3.5.6.3 - Quadratic forms
Section 2.3.5.7 - Decomposition (Factorization)
Section 2.3.5.7.0 - Decomposition (Factorization)
Section 2.3.5.7.1 - Matrix Decomposition
Section 2.3.5.7.1.0 - Basic Writeup - Wikipedia - Matrix Decomposition
Section 2.3.5.7.1.1 - Decompositions Related to Solving Systems of Linear Equations
Section 2.3.5.7.1.1.1 - LU Decomposition
Section 2.3.5.7.1.1.2 - LU Reduction
Section 2.3.5.7.1.1.3 - Block LU Reduction
Section 2.3.5.7.1.1.4 - Rank Factorization
Section 2.3.5.7.1.1.5 - Cholesky Decomp
Section 2.3.5.7.1.1.6 - QR Decomp
Section 2.3.5.7.1.1.7 - RRQR Decomp
Section 2.3.5.7.1.1.8 - Interpolative Decomp
Section 2.3.5.7.1.1.8 - Crout matrix decomposition
Section 2.3.5.7.1.2 - Decompositions Related to Eigenvalues and Related Concepts
Section 2.3.5.7.1.2.1 - Eigen Decomp
Section 2.3.5.7.1.2.2 - Jordan-Chevalley Decomp
Section 2.3.5.7.1.2.3 - Schur Decomp
Section 2.3.5.7.1.2.4 - Real Schur Decomp
Section 2.3.5.7.1.2.5 - Takagi's Factorization
Section 2.3.5.7.1.2.6 - QZ Decomp
Section 2.3.5.7.1.2.7 - Singular Value Decomp
Section 2.3.5.7.1.2.8 - Scale Invariant Decompositions
Section 2.3.5.7.1.3 - Other Decomposition Techniques
Section 2.3.5.7.1.3.1 - Polar Decomposition
Section 2.3.5.7.1.3.2 - Algebraic Polar Decomposition
Section 2.3.5.7.1.3.3 - Mostow's decomposition
Section 2.3.5.7.1.3.4 - Sinkhorn normal form
Section 2.3.5.7.1.3.5 - Sectoral decomposition
Section 2.3.5.7.1.3.6 - Williamson's normal form
Section 2.3.6 - Structures
Section 2.3.6.1 - Nullspace, range
Section 2.3.6.2 - Metric spaces
Section 2.3.6.3 - Normed spaces
Section 2.3.6.4 - Semi-Normed spaces
Section 2.3.6.5 - Inner product spaces
Section 2.3.6.5.0 - Basic Writeup - Wikipedia - Inner product spaces
Section 2.3.6.5.1 - Cauchy-Schwarz inequality
Section 2.3.6.5.2 - Orthogonality
Section 2.3.6.5.3 - Orthogonal complement
Section 2.3.6.5.4 - Orthogonal projection
Section 2.3.6.5.5 - Orthogonal group
Section 2.3.6.6 - Eigen Spaces
Section 2.3.6.7 - Topological vector space
Section 2.3.6.8 - Pseudo-Euclidean space
Section 2.3.6.8.0 - Basic Writeup - Wikipedia - Pseudo-Euclidean space
Section 2.3.6.8.1 - Null vector
Section 2.3.6.8.2 - Indefinite orthogonal group
Section 2.3.6.9 - Orientation (geometry)
Section 2.3.6.9.0 - Basic Writeup - Wikipedia - Orientation (geometry)
Section 2.3.6.9.1 - Improper rotation
Section 2.3.6.10 - Symplectic structure
Section 2.3.7 - Multi-Linear Algebra
Section 2.3.7.0 - Basic Writeup - Wikipedia - Multi-Linear Algebra
Section 2.3.7.1 - p-Vectors and Multivectors
Section 2.3.7.2 - Multilinear Map
Section 2.3.7.2.0 - Basic Writeup - Wikipedia - Multilinear Map
Section 2.3.7.2.1 - Bilinear Map
Section 2.3.7.2.2 - Bilinear Operators
Section 2.3.7.2.3 - Multilinear Form
Section 2.3.7.2.4 - Multilinear Subspace Learning
Section 2.3.7.3 - Exterior Algebra
Section 2.3.7.4 - Exterior Algebra
Section 2.3.7.5 - Exterior Derivative
Section 2.3.7.6 - Tensors
Section 2.3.7.6.0 - Basic Writeup - Wikipedia - Tensors
Section 2.3.7.6.1 - Classical treatment of Tensors
Section 2.3.7.6.2 - Component-free treatment of tensors
Section 2.3.7.6.3 - Mathematical Scope of Tensors
Section 2.3.7.6.3.1 - Coordinate System
Section 2.3.7.6.3.2 - Multilinear Algebra
Section 2.3.7.6.3.3 - Euclidean Geometry
Section 2.3.7.6.3.4 - Tensor Algebra
Section 2.3.7.6.3.5 - Dyadic Algebra
Section 2.3.7.6.3.6 - Dyadic Algebra
Section 2.3.7.6.3.7 - Differential Geometry
Section 2.3.7.6.3.8 - Exterior Calculus
Section 2.3.7.6.3.9 - Tensor Calculus
Section 2.3.7.6.4 - Tensor Notation
Section 2.3.7.6.4.1 - Index Notation
Section 2.3.7.6.4.2 - Multi-Index Notation
Section 2.3.7.6.4.3 - Einstein Notation
Section 2.3.7.6.4.4 - Ricci Calculus
Section 2.3.7.6.4.5 - Penrose Graphical Notation
Section 2.3.7.6.4.6 - Voigt Notation
Section 2.3.7.6.4.7 - Abstract Index Notation
Section 2.3.7.6.4.8 - Tetrad(Index) Notation
Section 2.3.7.6.4.9 - Van der Waerden Notation
Section 2.3.7.6.5 - Tensor Definitions
Section 2.3.7.6.5.1 - Tensor (Intrinsic Definition)
Section 2.3.7.6.5.2 - Tensor Field
Section 2.3.7.6.5.3 - Tensor Density
Section 2.3.7.6.5.4 - Tensors In Curvilinear Coordinates
Section 2.3.7.6.5.5 - Tensor Operator
Section 2.3.7.6.5.6 - Tensor Bundle
Section 2.3.7.6.5.7 - Two-Point Tensor
Section 2.3.7.6.6 - Some Noteable Tensors
Section 2.3.7.6.6.1 - Metric Tensor
Section 2.3.7.6.6.2 - Mixed Tensor
Section 2.3.7.6.6.3 - Symmetric Tensor
Section 2.3.7.6.6.4 - Antisymmetric Tensor
Section 2.3.7.6.6.5 - Dyadic Tensor
Section 2.3.7.6.6.6 - Kronecker Delta
Section 2.3.7.6.6.7 - Levi-Civita Symbol
Section 2.3.7.6.6.8 - Nonmetricity Tensor
Section 2.3.7.6.6.9 - Christoffel Symbols
Section 2.3.7.6.6.10 - Ricci Curvature
Section 2.3.7.6.6.11 - Riemann Curvature Tensor
Section 2.3.7.6.6.12 - Weyl Tensor
Section 2.3.7.6.6.13 - Torsion Tensor
Section 2.3.7.6.7 - Tensor Operations
Section 2.3.7.6.7.1 - Tensor Product
Section 2.3.7.6.7.2 - Tensor Contraction
Section 2.3.7.6.7.3 - Tensor Algebra
Section 2.3.7.6.7.3.0 - Basic Writeup - Wikipedia - Tensor Algebra
Section 2.3.7.6.7.3.1 - Exterior (Grassmann) Algebra
Section 2.3.7.6.7.3.1.0 - Basic Writeup - Exterior (Grassmann) Algebra
Section 2.3.7.6.7.3.1.1 - Exterior Product
Section 2.3.7.6.7.3.1.2 - Exterior Power
Section 2.3.7.6.7.3.2 - Symmetric Algebra
Section 2.3.7.6.7.3.3 - Clifford Algebra
Section 2.3.7.6.7.3.4 - Geometric Algebra
Section 2.3.7.6.7.4 - Transpose (2nd Order Tensors)
Section 2.3.7.6.7.5 - Raising and Lowering Indices
Section 2.3.7.6.7.6 - Hodge Star Operator
Section 2.3.7.6.7.7 - Covariant Derivative
Section 2.3.7.6.7.8 - Exterior Derivative
Section 2.3.7.6.7.9 - Exterior Covariant Derivative
Section 2.3.7.6.7.10 - Lie Derivative
Section 2.3.8 - Affine Space
Section 2.3.8.0 - Basic Writeup - Wikipedia - Affine Space
Section 2.3.8.1 - Affine transformation
Section 2.3.8.2 - Affine group
Section 2.3.8.3 - Affine geometry
Section 2.3.8.4 - Affine coordinate system
Section 2.3.8.5 - Flat (geometry)
Section 2.3.8.6 - Cartesian coordinate system
Section 2.3.8.7 - Euclidean group
Section 2.3.8.8 - Poincaré group
Section 2.3.8.9 - Galilean group
Section 2.3.9 - Projective Space
Section 2.3.9.0 - Basic Writeup - Wikipedia - Projective Space
Section 2.3.9.1 - Projective transformation
Section 2.3.9.2 - Projective geometry
Section 2.3.9.3 - Projective linear group
Section 2.3.9.4 - Quadric Section
Section 2.3.9.5 - Conic Section
Section 2.3.10 - Numerical Linear Algebra
Section 2.3.10.0 - Basic Writeup - Wikipedia - Numerical Linear Algebra
Section 2.3.10.1 - Basic Concepts in Numerical Linear Algebra
Section 2.3.10.1.1 - Types of matrices appearing in numerical analysis
Section 2.3.10.1.1.1 - Sparse matrix
Section 2.3.10.1.1.1.0 - Basic Writeup - Wikipedia - Sparse matrix
Section 2.3.10.1.1.1.1 - Band matrix
Section 2.3.10.1.1.1.2 - Bidiagonal matrix
Section 2.3.10.1.1.1.3 - Tridiagonal matrix
Section 2.3.10.1.1.1.4 - Pentadiagonal matrix
Section 2.3.10.1.1.1.5 - Skyline matrix
Section 2.3.10.1.1.2 - Circulant matrix
Section 2.3.10.1.1.3 - Triangular matrix
Section 2.3.10.1.1.4 - Diagonally dominant matrix
Section 2.3.10.1.1.5 - Block matrix
Section 2.3.10.1.1.6 - Stieltjes matrix
Section 2.3.10.1.1.7 - Hilbert matrix
Section 2.3.10.1.1.8 - Wilkinson matrix
Section 2.3.10.1.1.9 - Convergent matrix
Section 2.3.10.1.2 - Algorithms for matrix multiplication
Section 2.3.10.1.2.1 - Strassen algorithm
Section 2.3.10.1.2.2 - Coppersmith–Winograd algorithm
Section 2.3.10.1.2.3 - Cannon's algorithm
Section 2.3.10.1.2.4 - Freivalds' algorithm
Section 2.3.10.1.3 - Matrix decompositions (See Chapter 4.5.7.1 for Matrix Decomposition Details)
Section 2.3.10.2 - Solving Linear Systems of Equations
Section 2.3.10.2.0 - Basic Writeup - Wikibooks - Solving Linear Systems
Section 2.3.10.2.1 - Gauss' Method
Section 2.3.10.2.2 - Describing the Solution Set
Section 2.3.10.2.3 - General = Particular + Homogeneous
Section 2.3.10.2.4 - Comparing Set Descriptions
Section 2.3.10.2.5 - Automation
Section 2.3.10.2.6 - Gaussian elimination
Section 2.3.10.2.6.0 - Basic Writeup - Wikipedia - Gaussian elimination
Section 2.3.10.2.6.1 - Row echelon form
Section 2.3.10.2.6.2 - Bareiss algorithm
Section 2.3.10.2.6.3 - Tridiagonal matrix algorithm
Section 2.3.10.2.7 - Solving Linear Equations through Factorization(Decomposition - See Section 2.3.5.7)
Section 2.3.10.2.7.1 - LU decomposition
Section 2.3.10.2.7.1.0 - Basic Writeup - Wikipedia - LU decomposition
Section 2.3.10.2.7.1.1 - Crout matrix decomposition
Section 2.3.10.2.7.1.2 - LU reduction
Section 2.3.10.2.7.1.3 - Block LU decomposition
Section 2.3.10.2.7.2 - Rank Factorization
Section 2.3.10.2.7.3 - QR Decomp
Section 2.3.10.2.7.4 - RRQR Decomp
Section 2.3.10.2.7.5 - Interpolative Decomp
Section 2.3.10.2.7.6 - Cholesky decomposition
Section 2.3.10.2.7.6.0 - Basic Writeup - Wikipedia - Cholesky decomposition
Section 2.3.10.2.7.6.1 - Minimum degree algorithm
Section 2.3.10.2.7.6.2 - Symbolic Cholesky decomposition
Section 2.3.10.2.8 - Iterative refinement
Section 2.3.10.2.9 - Direct methods for sparse matrices
Section 2.3.10.2.9.1 - Frontal Solver
Section 2.3.10.2.9.2 - Nested dissection
Section 2.3.10.2.10 - Levinson recursion for Toeplitz matrices
Section 2.3.10.2.11 - SPIKE algorithm
Section 2.3.10.2.12 - Cyclic reduction
Section 2.3.10.2.13 - Iterative methods
Section 2.3.10.2.13.1 - Jacobi method
Section 2.3.10.2.13.2 - Gauss–Seidel method
Section 2.3.10.2.13.2.0 - Basic Writeup - Wikipedia - Gauss–Seidel method
Section 2.3.10.2.13.2.1 - Successive over-relaxation (SOR)
Section 2.3.10.2.13.2.1.0 - Basic Writeup - Wikipedia - Successive over-relaxation (SOR)
Section 2.3.10.2.13.2.1.1 - Symmetric successive overrelaxation (SSOR)
Section 2.3.10.2.13.2.2 - Backfitting algorithm
Section 2.3.10.2.13.3 - Modified Richardson iteration
Section 2.3.10.2.13.4 - Conjugate gradient method (CG)
Section 2.3.10.2.13.4.0 - Basic Writeup - Wikipedia - Conjugate gradient method (CG)
Section 2.3.10.2.13.4.1 - Derivation of the conjugate gradient method
Section 2.3.10.2.13.4.2 - Nonlinear conjugate gradient method
Section 2.3.10.2.13.5 - Biconjugate gradient method (BiCG)
Section 2.3.10.2.13.5.0 - Basic Writeup - Wikipedia - Biconjugate gradient method (BiCG)
Section 2.3.10.2.13.5.1 - Biconjugate Gradient Stabilized Method(BiCGSTAB)
Section 2.3.10.2.13.6 - Conjugate residual method
Section 2.3.10.2.13.7 - Generalized minimal residual method (GMRES)
Section 2.3.10.2.13.8 - Chebyshev iteration
Section 2.3.10.2.13.9 - Stone's method (SIP – Srongly Implicit Procedure)
Section 2.3.10.2.13.10 - Kaczmarz method
Section 2.3.10.2.13.11 - Preconditioner
Section 2.3.10.2.13.11.0 - Basic Writeup - Wikipedia - Preconditioner
Section 2.3.10.2.13.11.1 - Incomplete Cholesky factorization
Section 2.3.10.2.13.11.2 - Incomplete LU factorization
Section 2.3.10.2.13.12 - Uzawa iteration
Section 2.3.10.2.14 - Underdetermined and overdetermined systems
Section 2.3.10.2.14.1 - Numerical computation of null space
Section 2.3.10.2.14.2 - Moore–Penrose pseudoinverse
Section 2.3.10.2.14.3 - Sparse approximation
Section 2.3.10.3 - Eigenvalue Algorithms
Section 2.3.10.3.0 - Basic Writeup - Wikipedia - Eigenvalue Algorithms
Section 2.3.10.3.1 - Power iteration
Section 2.3.10.3.2 - Inverse iteration
Section 2.3.10.3.3 - Rayleigh quotient iteration
Section 2.3.10.3.4 - Arnoldi iteration
Section 2.3.10.3.5 - Lanczos algorithm
Section 2.3.10.3.5.0 - Basic Writeup - Wikipedia - Lanczos algorithm
Section 2.3.10.3.5.1 - Block Lanczos algorithm
Section 2.3.10.3.6 - QR algorithm
Section 2.3.10.3.7 - Jacobi eigenvalue algorithm
Section 2.3.10.3.7.0 - Basic Writeup - Wikipedia - Jacobi eigenvalue algorithm
Section 2.3.10.3.7.1 - Jacobi rotation
Section 2.3.10.3.7.2 - Jacobi method for complex Hermitian matrices
Section 2.3.10.3.8 - Divide-and-conquer eigenvalue algorithm
Section 2.3.10.3.9 - Folded spectrum method
Section 2.3.10.3.10 - Locally Optimal Block Preconditioned Conjugate Gradient Method(LOBPCG)
Section 2.3.10.3.11 - Eigenvalue perturbation
Section 2.3.10.4 - Other Concepts and Algorithms
Section 2.3.10.4.1 - Orthogonalization algorithms
Section 2.3.10.4.1.0 - Basic Writeup - Wikipedia - Orthogonalization algorithms
Section 2.3.10.4.1.1 - Gram–Schmidt process
Section 2.3.10.4.1.2 - Householder transformation
Section 2.3.10.4.1.2.0 - Basic Writeup - Wikipedia - Householder transformation
Section 2.3.10.4.1.2.1 - Householder operator
Section 2.3.10.4.1.3 - Givens rotation
Section 2.3.10.4.2 - Krylov subspace
Section 2.3.10.4.3 - Block matrix pseudoinverse
Section 2.3.10.4.4 - Bidiagonalization
Section 2.3.10.4.5 - Cuthill–McKee algorithm
Section 2.3.10.4.6 - In-place matrix transposition
Section 2.3.10.4.7 - Pivot element
Section 2.3.10.4.8 - Matrix-free methods
Section 2.4.0 - Introductory Writeups
Section 2.4.0.1 - Basic Writeups
Section 2.4.0.1.1 - Part 1 - Katariya - Introduction to Calculus
Section 2.4.0.1.2 - Part 2 - Wikibooks - Calculus
Section 2.4.0.1.3 - Part 3 - Wikipedia - Glossary of Calculus
Section 2.4.0.1.4 - Part 4 - Wikipedia - Calculus
Section 2.4.0.1.5 - Part 5 - Wikipedia - Outline of Calculus
Section 2.4.0.2 - Detailed Writeups
Section 2.4.0.2.1 - Part 1 - Whitman - Single and Multivariable Calculus
Section 2.4.0.2.2 - Part 2 - Shurman,College - Multivariable Calculus
Section 2.4.0.2.3 - Part 3 - Calin - An Introduction to Stochastic Calculus with Applications to Finance
Section 2.4.0.2.4 - Part 4 - Marsden,Tromba - Vector Calculus
Section 2.4.0.2.5 - Part 5 - Loomis,Sternberg - Advanced Calculus
Section 2.4.0.2.6 - Part 6 - Grinfeld - Introduction to Tensor Analysis and the Calculus of Moving Surfaces
Section 2.4.0.2.7 - Part 7 - Edwards,Penney - Elementary Differential Equations
Section 2.4.0.2.8 - Part 8 - Barendregt,Barendsen - Introduction to Lambda Calculus
Section 2.4.0.2.9 - Part 9 - Bennewitz - Complex Analysis
Section 2.4.0.2.10 - Part 10 - Berg - Complex Analysis
Section 2.4.0.2.11 - Part 11 - Beck,Marchesi,Pixton,Sabalka - First course in Complex Analysis
Section 2.4.0.3 - Videos
Section 2.4.0.3.1 - Part 1 - Khan Academy - Calculus
Section 2.4.0.3.2 - Part 2 - 3Blue1Brown - Essence of Calculus
Section 2.4.0.3.3 - Part 3 - MIT - Single Variable Calculus
Section 2.4.0.3.4 - Part 4 - MIT - Multi Variable Calculus
Section 2.4.0.3.5 - Part 5 - Khan Academy - Multi Variable Calculus
Section 2.4.0.3.6 - Part 6 - Khan Academy - Calculus of Variations
Section 2.4.0.3.7 - Part 7 - MIT - Calculus of Complex Variables
Section 2.4.0.3.8 - Part 8 - MIT - Vector Calculus
Section 2.4.0.3.9 - Part 9 - MIT - Tensor Calculus
Section 2.4.0.3.10 - Part 10 - MIT - Stochastic Calculus
Section 2.4.0.3.11 - Part 11 - MIT - Differential Equations
Section 2.4.0.3.12 - Part 12 - PLT - Lambda Calculus
Section 2.4.0.3.13 - Part 13 - Khan Academy - Integrals
Section 2.4.0.3.14 - Part 14 - Khan Academy - Partial Derivatives
Section 2.4.0.3.15 - Part 15 - Math The Beautiful - Partial Derivatives
Section 2.4.0.3.16 - Part 16 - Khan Academy - Hessian Matrix
Section 2.4.0.3.17 - Part 17 - Khan Academy - Jacobian Matrix
Section 2.4.0.3.18 - Part 18 - Khan Academy - Laplacian Transforms
Section 2.4.1 - Branches of Calculus
Section 2.4.1.1 - Differential calculus
Section 2.4.1.2 - Integral calculus
Section 2.4.1.3 - Multivariable calculus
Section 2.4.1.4 - Stochastic calculus
Section 2.4.1.5 - Multiplicative calculus
Section 2.4.1.6 - Non Standard calculus
Section 2.4.1.7 - Series
Section 2.4.1.8 - Vector Calculus
Section 2.4.1.9 - Malliavin calculus
Section 2.4.1.10 - Fractional calculus
Section 2.4.1.11 - Calculus of Variations
Section 2.4.2 - General Calculus Concepts
Section 2.4.2.1 - Fundamental Theorem of Calculus
Section 2.4.2.2 - Limits of Functions
Section 2.4.2.3 - Continuous function
Section 2.4.2.4 - Mean value theorem
Section 2.4.2.5 - Rolle's theorem
Section 2.4.2.6 - Derivative
Section 2.4.2.7 - Antiderivative
Section 2.4.2.8 - Integral
Section 2.4.2.9 - Improper Integral
Section 2.4.2.10 - Infinitesimals
Section 2.4.2.11 - Partial derivative
Section 2.4.2.12 - Multiple Intergral
Section 2.4.3 - Limits
Section 2.4.3.0 - Basic Writeup - Wikipedia - Limits
Section 2.4.3.1 - An Introduction to Limits
Section 2.4.3.2 - Limit of a Function
Section 2.4.3.3 - Formal Definition of the Limit
Section 2.4.3.4 - Finite Limits
Section 2.4.3.4.0 - Basic Writeup - Wikibooks - Finite Limits
Section 2.4.3.4.1 - One Sided Limit
Section 2.4.3.5 - Infinite Limits
Section 2.4.3.6 - Limit of a Sequence
Section 2.4.3.7 - Continuity
Section 2.4.3.8 - Proofs of Some Basic Limit Rules
Section 2.4.3.9 - Indeterminate Form
Section 2.4.3.10 - Orders of approximation
Section 2.4.3.11 - (ε, δ)-definition of limit
Section 2.4.3.12 - Limit Excercises
Section 2.4.4 - Derivative(Differentiation)
Section 2.4.4.1 - Basics
Section 2.4.4.1.1 - Differential Calculus
Section 2.4.4.1.1.0 - Basic Writeup - Differential Calculus
Section 2.4.4.1.1.1 - Differential
Section 2.4.4.1.1.1.0 - Basic Writeup - Differential
Section 2.4.4.1.1.1.0.1 - Part 1 - Wikipedia - Differential
Section 2.4.4.1.1.1.0.2 - Part 2 - Wikibooks - Differentiation Defined
Section 2.4.4.1.1.1.1 - Differential in terms of the Infinitesimal
Section 2.4.4.1.1.1.2 - Differential of a Function
Section 2.4.4.1.1.1.3 - Total Differential
Section 2.4.4.1.1.1.4 - Simple Rules and Identities
Section 2.4.4.1.1.1.4.0 - Basic Writeup - Wikipedia - Differentiation Rules
Section 2.4.4.1.1.1.4.1 - Product and Quotient Rules
Section 2.4.4.1.1.1.4.2 - Chain Rule
Section 2.4.4.1.1.1.4.3 - Derivative of a Constant
Section 2.4.4.1.1.1.4.4 - Sum rule in differentiation
Section 2.4.4.1.1.1.4.5 - Constant factor rule in differentiation
Section 2.4.4.1.1.1.4.6 - Linearity of differentiation
Section 2.4.4.1.1.1.4.7 - Power rule
Section 2.4.4.1.1.1.4.8 - Inverse rule
Section 2.4.4.1.1.1.4.9 - General Leibniz Rule
Section 2.4.4.1.1.1.4.10 - Faà di Bruno's formula
Section 2.4.4.1.1.1.4.11 - L'Hôpital's rule
Section 2.4.4.1.1.1.5 - Differential Notation
Section 2.4.4.1.1.1.6 - Differential equation
Section 2.4.4.1.1.1.7 - Differential Operator
Section 2.4.4.1.1.1.8 - Implicit Differentiation
Section 2.4.4.1.1.1.9 - Inverse functions and differentiation
Section 2.4.4.1.1.2 - Derivative
Section 2.4.4.1.1.2.0 - Basic Writeup - Wikipedia - Derivative
Section 2.4.4.1.1.2.1 - Generalizations of the Derivative
Section 2.4.4.1.1.2.2 - Derivatives of Exponential and Logarithm Functions
Section 2.4.4.1.1.2.3 - Logarithmic derivatives
Section 2.4.4.1.1.2.4 - Derivatives of Trigonometric Functions
Section 2.4.4.1.1.2.5 - Derivatives of hyperbolic functions
Section 2.4.4.1.1.2.6 - Derivatives of special functions
Section 2.4.4.1.1.2.7 - Derivatives of integrals
Section 2.4.4.1.1.2.8 - Higher Order Derivatives
Section 2.4.4.1.1.2.8.0 - Basic Writeup - Wikibooks - Higher Order Derivatives
Section 2.4.4.1.1.2.8.1 - Second derivative
Section 2.4.4.1.1.2.8.2 - Third derivative
Section 2.4.4.1.1.2.8.3 - Faà di Bruno's formula
Section 2.4.4.1.1.2.8.4 - General Leibniz rule
Section 2.4.4.1.2 - Some Important Theorems
Section 2.4.4.1.2.0 - Basic Writeup - Wikibooks - Some Important Theorems
Section 2.4.4.1.2.1 - Taylor's theorem
Section 2.4.4.1.2.2 - Rolle's theorem
Section 2.4.4.1.2.3 - Mean Value Theorem
Section 2.4.4.1.2.4 - Extreme Value Theorem
Section 2.4.4.1.2.5 - Newton's Method
Section 2.4.4.1.3 - Notation
Section 2.4.4.1.3.0 - Basic Writeup - Wikipedia - Notation
Section 2.4.4.1.3.1 - Newton's notation for differentiation
Section 2.4.4.1.3.2 - Leibniz's notation for differentiation
Section 2.4.4.1.4 - Change of variables
Section 2.4.4.1.5 - Related rates
Section 2.4.4.1.6 - Stationary point
Section 2.4.4.1.6.0 - Basic Writeup - Wikipedia - Stationary point
Section 2.4.4.1.6.1 - Maxima and minima
Section 2.4.4.1.6.2 - First derivative test
Section 2.4.4.1.6.3 - Second derivative test
Section 2.4.4.1.6.4 - Extreme value theorem
Section 2.4.4.1.7 - Exercises
Section 2.4.4.2 - Applications of Derivatives
Section 2.4.4.2.1 - L'Hôpital's Rule
Section 2.4.4.2.2 - Extrema and Points of Inflection
Section 2.4.4.2.3 - Newton's Method
Section 2.4.4.2.4 - Related Rates
Section 2.4.4.2.5 - Optimization
Section 2.4.4.2.6 - Euler's Method
Section 2.4.4.2.7 - Exercises
Section 2.4.4.3 - Numerical methods for ordinary differential equations
Section 2.4.4.3.0 - Basic Writeup - Wikipedia - Numerical methods for ordinary differential equations
Section 2.4.4.3.1 - Euler method
Section 2.4.4.3.2 - Explicit and implicit methods
Section 2.4.4.3.3 - Backward Euler method
Section 2.4.4.3.4 - Trapezoidal rule
Section 2.4.4.3.5 - Runge–Kutta methods
Section 2.4.4.3.5.0 - Basic Writeup - Wikipedia - Runge–Kutta methods
Section 2.4.4.3.5.1 - Midpoint method
Section 2.4.4.3.5.2 - Heun's method
Section 2.4.4.3.5.3 - Bogacki–Shampine method
Section 2.4.4.3.5.4 - Cash–Karp method
Section 2.4.4.3.5.5 - Dormand–Prince method
Section 2.4.4.3.5.6 - Runge–Kutta–Fehlberg method
Section 2.4.4.3.5.7 - Gauss–Legendre method
Section 2.4.4.3.5.8 - Butcher group
Section 2.4.4.3.5.9 - List of Runge–Kutta methods
Section 2.4.4.3.6 - Linear multistep method
Section 2.4.4.3.6.0 - Basic Writeup - Wikipedia - Linear multistep method
Section 2.4.4.3.6.1 - Backward differentiation formula
Section 2.4.4.3.6.2 - Numerov's method
Section 2.4.4.3.6.3 - Predictor–corrector method
Section 2.4.4.3.7 - General linear methods
Section 2.4.4.3.8 - Bulirsch–Stoer algorithm
Section 2.4.4.3.9 - Exponential integrator
Section 2.4.4.3.10 - Methods designed for the solution of ODEs from classical physics
Section 2.4.4.3.10.1 - Newmark-beta method
Section 2.4.4.3.10.2 - Verlet integration
Section 2.4.4.3.10.3 - Leapfrog integration
Section 2.4.4.3.10.4 - Beeman's algorithm
Section 2.4.4.3.10.5 - Dynamic relaxation
Section 2.4.4.3.11 - Geometric integrator
Section 2.4.4.3.11.0 - Basic Writeup - Wikipedia - Geometric integrator
Section 2.4.4.3.11.1 - Symplectic integrator
Section 2.4.4.3.11.1.0 - Basic Writeup - Wikipedia - Symplectic integrator
Section 2.4.4.3.11.1.1 - Variational integrator
Section 2.4.4.3.11.1.2 - Semi-implicit Euler method
Section 2.4.4.3.11.2 - Energy drift
Section 2.4.4.3.12 - Other methods for initial value problems (IVPs)
Section 2.4.4.3.12.1 - Bi-directional delay line
Section 2.4.4.3.12.2 - Partial element equivalent circuit
Section 2.4.4.3.13 - Methods for solving two-point boundary value problems (BVPs)
Section 2.4.4.3.13.1 - Shooting method
Section 2.4.4.3.13.2 - Direct multiple shooting method
Section 2.4.4.3.14 - Methods for solving differential-algebraic equations (DAEs - ODE's with Constraints)
Section 2.4.4.3.14.1 - Constraint algorithm
Section 2.4.4.3.14.2 - Pantelides algorithm
Section 2.4.4.3.15 - Methods for solving stochastic differential equations (SDEs)
Section 2.4.4.3.15.1 - Euler–Maruyama method
Section 2.4.4.3.15.2 - Milstein method
Section 2.4.4.3.15.3 - Runge–Kutta method (SDE)
Section 2.4.4.3.16 - Methods for solving integral equations
Section 2.4.4.3.16.1 - Nyström method
Section 2.4.4.3.17 - Analysis
Section 2.4.4.3.17.1 - Truncation error (numerical integration)
Section 2.4.4.3.17.1.0 - Basic Writeup - Wikipedia - Truncation error (numerical integration)
Section 2.4.4.3.17.1.1 - Lady Windermere's Fan (mathematics)
Section 2.4.4.3.18 - Stiff equation
Section 2.4.4.3.18.0 - Basic Writeup - Wikipedia - Stiff equation
Section 2.4.4.3.18.1 - L-stability
Section 2.4.4.3.18.2 - Dynamic errors of numerical methods of ODE discretization
Section 2.4.4.3.19 - Adaptive stepsize
Section 2.4.4.3.20 - Parareal
Section 2.4.4.4 - Numerical Methods for Partial Differential Equations
Section 2.4.4.4.1 - Finite difference methods
Section 2.4.4.4.1.0 - Basic Writeup - Wikipedia - Finite difference methods
Section 2.4.4.4.1.1 - Finite difference
Section 2.4.4.4.1.1.0 - Basic Writeup - Wikipedia - Finite difference
Section 2.4.4.4.1.1.1 - Finite difference coefficient
Section 2.4.4.4.1.1.2 - Discrete Laplace operator
Section 2.4.4.4.1.1.2.0 - Basic Writeup - Wikipedia - Discrete Laplace operator
Section 2.4.4.4.1.1.2.1 - Eigenvalues and eigenvectors of the second derivative
Section 2.4.4.4.1.1.2.2 - Kronecker sum of discrete Laplacians
Section 2.4.4.4.1.1.3 - Discrete Poisson equation
Section 2.4.4.4.1.2 - Stencil (numerical analysis)
Section 2.4.4.4.1.2.0 - Basic Writeup - Wikipedia - Stencil (numerical analysis)
Section 2.4.4.4.1.2.1 - Compact stencil
Section 2.4.4.4.1.2.1.0 - Basic Writeup - Wikipedia - Compact stencil
Section 2.4.4.4.1.2.1.1 - Higher-order compact finite difference scheme
Section 2.4.4.4.1.2.2 - Non-compact stencil
Section 2.4.4.4.1.2.3 - Five-point stencil
Section 2.4.4.4.1.3 - Finite difference methods for heat equation and related PDEs
Section 2.4.4.4.1.3.1 - FTCS scheme (forward-time central-space)
Section 2.4.4.4.1.3.2 - Crank–Nicolson method
Section 2.4.4.4.1.4 - Finite difference methods for hyperbolic PDEs like the wave equation
Section 2.4.4.4.1.4.1 - Lax–Friedrichs method
Section 2.4.4.4.1.4.2 - Lax–Wendroff method
Section 2.4.4.4.1.4.3 - MacCormack method
Section 2.4.4.4.1.4.4 - Upwind scheme
Section 2.4.4.4.1.4.4.0 - Basic Writeup - Wikipedia - Upwind scheme
Section 2.4.4.4.1.4.4.1 - Upwind differencing scheme for convection
Section 2.4.4.4.1.4.5 - Lax–Wendroff theorem
Section 2.4.4.4.1.5 - Alternating direction implicit method (ADI)
Section 2.4.4.4.1.6 - Nonstandard finite difference scheme
Section 2.4.4.4.1.7 - Specific applications
Section 2.4.4.4.1.7.1 - Finite difference methods for option pricing
Section 2.4.4.4.1.7.2 - Finite-difference time-domain method
Section 2.4.4.4.2 - Finite element methods, gradient discretisation methods
Section 2.4.4.4.2.0 - Basic Writeups
Section 2.4.4.4.2.0.1 - Part 1 - Wikipedia - Finite element methods
Section 2.4.4.4.2.0.2 - Part 2 - Wikipedia - Gradient Discretisation Methods
Section 2.4.4.4.2.1 - Finite element method in structural mechanics
Section 2.4.4.4.2.2 - Galerkin method
Section 2.4.4.4.2.2.0 - Basic Writeup - Wikipedia - Galerkin method
Section 2.4.4.4.2.2.1 - Discontinuous Galerkin method
Section 2.4.4.4.2.3 - Rayleigh–Ritz method
Section 2.4.4.4.2.4 - Spectral element method
Section 2.4.4.4.2.5 - hp-FEM
Section 2.4.4.4.2.6 - Examples of finite elements
Section 2.4.4.4.2.6.1 - Bilinear quadrilateral element
Section 2.4.4.4.2.6.2 - Constant strain triangle element (CST)
Section 2.4.4.4.2.6.3 - Quadratic quadrilateral element
Section 2.4.4.4.2.6.4 - Barsoum elements
Section 2.4.4.4.2.7 - Direct stiffness method
Section 2.4.4.4.2.8 - Trefftz method
Section 2.4.4.4.2.9 - Finite element updating
Section 2.4.4.4.2.10 - Extended finite element method
Section 2.4.4.4.2.11 - Functionally graded elements
Section 2.4.4.4.2.12 - Superelement
Section 2.4.4.4.2.13 - Interval finite element method
Section 2.4.4.4.2.14 - Discrete exterior calculus
Section 2.4.4.4.2.15 - Modal analysis using FEM
Section 2.4.4.4.2.16 - Céa's lemma
Section 2.4.4.4.2.17 - Patch test (finite elements)
Section 2.4.4.4.2.19 - Multiphase topology optimisation
Section 2.4.4.4.2.20 - Interval finite element
Section 2.4.4.4.2.21 - Applied element method
Section 2.4.4.4.2.22 - Wood–Armer method
Section 2.4.4.4.2.23 - Isogeometric analysis
Section 2.4.4.4.2.24 - Loubignac iteration
Section 2.4.4.4.2.25 - Stiffness matrix
Section 2.4.4.4.2.26 - Combination with meshfree methods
Section 2.4.4.4.2.27.1 - Weakened weak form
Section 2.4.4.4.2.27.2 - G space
Section 2.4.4.4.2.27.3 - Smoothed finite element method
Section 2.4.4.4.2.27 - Variational multiscale method
Section 2.4.4.4.2.28 - Variational multiscale method
Section 2.4.4.4.3 - Other methods
Section 2.4.4.4.3.1 - Spectral method
Section 2.4.4.4.3.1.0 - Basic Writeup - Wikipedia - Spectral method
Section 2.4.4.4.3.1.1 - Pseudo-spectral method
Section 2.4.4.4.3.2 - Method of lines
Section 2.4.4.4.3.3 - Boundary element method (BEM)
Section 2.4.4.4.3.3.0 - Basic Writeup - Wikipedia - Boundary element method (BEM)
Section 2.4.4.4.3.3.1 - Interval boundary element method
Section 2.4.4.4.3.4 - Analytic element method
Section 2.4.4.4.3.5 - Finite volume method
Section 2.4.4.4.3.5.0 - Basic Writeup - Wikipedia - Finite volume method
Section 2.4.4.4.3.5.1 - Godunov's scheme
Section 2.4.4.4.3.5.2 - MUSCL scheme
Section 2.4.4.4.3.5.3 - Advection Upstream Splitting Method(AUSM)
Section 2.4.4.4.3.5.4 - Flux limiter
Section 2.4.4.4.3.5.5 - Riemann solver
Section 2.4.4.4.3.5.6 - Properties of discretization schemes
Section 2.4.4.4.3.6 - Discrete element method
Section 2.4.4.4.3.6.0 - Basic Writeup - Wikipedia - Discrete element method
Section 2.4.4.4.3.6.1 - Extended discrete element method
Section 2.4.4.4.3.6.2 - Movable cellular automaton
Section 2.4.4.4.3.7 - Meshfree methods
Section 2.4.4.4.3.7.0 - Basic Writeup - Wikipedia - Meshfree methods
Section 2.4.4.4.3.7.1 - Discrete least squares meshless method
Section 2.4.4.4.3.7.2 - Diffuse element method
Section 2.4.4.4.3.7.3 - Finite pointset method
Section 2.4.4.4.3.7.4 - Moving Particle Semi-implicit Method
Section 2.4.4.4.3.7.5 - Method of fundamental solutions (MFS)
Section 2.4.4.4.3.7.6 - Variants of MFS with source points on the physical boundary
Section 2.4.4.4.3.7.6.1 - Boundary knot method (BKM)
Section 2.4.4.4.3.7.6.2 - Boundary particle method (BPM)
Section 2.4.4.4.3.7.6.3 - Regularized meshless method (RMM)
Section 2.4.4.4.3.7.6.4 - Singular boundary method (SBM)
Section 2.4.4.4.3.8 - Methods designed for problems from electromagnetics
Section 2.4.4.4.3.8.1 - Finite-difference time-domain method
Section 2.4.4.4.3.8.2 - Rigorous coupled-wave analysis
Section 2.4.4.4.3.8.3 - Transmission-line matrix method (TLM)
Section 2.4.4.4.3.8.4 - Uniform theory of diffraction
Section 2.4.4.4.3.9 - Particle-in-cell
Section 2.4.4.4.3.9.0 - Basic Writeup - Wikipedia - Particle-in-cell
Section 2.4.4.4.3.9.1 - Multiphase particle-in-cell method
Section 2.4.4.4.3.10 - High-resolution scheme
Section 2.4.4.4.3.11 - Shock capturing method
Section 2.4.4.4.3.12 - Vorticity confinement
Section 2.4.4.4.3.13 - Split-step method
Section 2.4.4.4.3.14 - Fast marching method
Section 2.4.4.4.3.15 - Orthogonal collocation
Section 2.4.4.4.3.16 - Lattice Boltzmann methods
Section 2.4.4.4.3.17 - Roe solver
Section 2.4.4.4.3.18 - Relaxation (iterative method)
Section 2.4.4.4.3.19 - Broad classes of methods
Section 2.4.4.4.3.19.1 - Mimetic methods
Section 2.4.4.4.3.19.2 - Multiphysics methods
Section 2.4.4.4.3.19.3 - Immersed boundary method
Section 2.4.4.4.3.20 - Multisymplectic integrator
Section 2.4.4.4.3.21 - Stretched grid method
Section 2.4.4.4.4 - Techniques for improving these methods
Section 2.4.4.4.4.1 - Multigrid method
Section 2.4.4.4.4.2 - Domain decomposition methods
Section 2.4.4.4.4.2.0 - Basic Writeup - Wikipedia - Domain decomposition methods
Section 2.4.4.4.4.2.1 - Additive Schwarz method
Section 2.4.4.4.4.2.2 - Abstract Additive Schwarz method
Section 2.4.4.4.4.2.3 - Balancing domain decomposition method (BDD)
Section 2.4.4.4.4.2.4 - Balancing domain decomposition by constraints (BDDC)
Section 2.4.4.4.4.2.5 - Finite element tearing and interconnect (FETI)
Section 2.4.4.4.4.2.6 - FETI-DP
Section 2.4.4.4.4.2.7 - Fictitious domain method
Section 2.4.4.4.4.2.8 - Mortar methods
Section 2.4.4.4.4.2.9 - Neumann–Dirichlet method
Section 2.4.4.4.4.2.10 - Neumann–Neumann methods
Section 2.4.4.4.4.2.11 - Poincaré–Steklov operator
Section 2.4.4.4.4.2.12 - Schur complement method
Section 2.4.4.4.4.2.13 - Schwarz alternating method
Section 2.4.4.4.4.3 - Coarse space
Section 2.4.4.4.4.4 - Adaptive mesh refinement
Section 2.4.4.4.4.5 - Fast multipole method
Section 2.4.4.4.4.6 - Perfectly matched layer
Section 2.4.4.4.5 - Grids and meshes
Section 2.4.4.4.5.1 - Grid Classifications and Types Of Meshes
Section 2.4.4.4.5.1.0 - Basic Writeups
Section 2.4.4.4.5.1.0.1 - Part 1 - Wikipedia - Grid Classification
Section 2.4.4.4.5.1.0.2 - Part 2 - Wikipedia - Types of Mesh
Section 2.4.4.4.5.1.1 - Polygon mesh
Section 2.4.4.4.5.1.2 - Triangle mesh
Section 2.4.4.4.5.1.2.0 - Basic Writeup - Wikipedia - Triangle mesh
Section 2.4.4.4.5.1.2.1 - Triangulation (geometry)
Section 2.4.4.4.5.1.2.2 - Nonobtuse mesh
Section 2.4.4.4.5.1.2.3 - Point set triangulation
Section 2.4.4.4.5.1.2.4 - Polygon triangulation
Section 2.4.4.4.5.1.2.5 - Delaunay triangulation
Section 2.4.4.4.5.1.2.6 - Constrained Delaunay triangulation
Section 2.4.4.4.5.1.2.7 - Pitteway triangulation
Section 2.4.4.4.5.1.2.8 - Minimum-weight triangulation
Section 2.4.4.4.5.1.2.9 - Kinetic triangulation
Section 2.4.4.4.5.1.2.10 - Triangulated irregular network
Section 2.4.4.4.5.1.2.11 - Quasi-triangulation
Section 2.4.4.4.5.1.3 - Volume mesh
Section 2.4.4.4.5.1.4 - Regular grid
Section 2.4.4.4.5.1.5 - Unstructured grid
Section 2.4.4.4.5.1.6 - Geodesic grid
Section 2.4.4.4.5.2 - Mesh generation
Section 2.4.4.4.5.2.0 - Basic Writeup - Wikipedia - Mesh generation
Section 2.4.4.4.5.2.1 - Image-based meshing
Section 2.4.4.4.5.2.2 - Marching cubes
Section 2.4.4.4.5.2.3 - Parallel mesh generation
Section 2.4.4.4.5.2.4 - Ruppert's algorithm
Section 2.4.4.4.5.3 - Subdivisions
Section 2.4.4.4.5.3.1 - Apollonian network
Section 2.4.4.4.5.3.2 - Barycentric subdivision
Section 2.4.4.4.5.4 - Improving an existing mesh
Section 2.4.4.4.5.4.1 - Chew's second algorithm
Section 2.4.4.4.5.4.2 - Laplacian smoothing
Section 2.4.4.4.5.5 - Jump-and-Walk algorithm
Section 2.4.4.4.5.6 - Spatial twist continuum
Section 2.4.4.4.5.7 - Pseudotriangle
Section 2.4.4.4.5.8 - Simplicial complex
Section 2.4.4.4.6 - Analysis
Section 2.4.4.4.6.1 - Lax equivalence theorem
Section 2.4.4.4.6.2 - Courant–Friedrichs–Lewy condition
Section 2.4.4.4.6.3 - Von Neumann stability analysis
Section 2.4.4.4.6.4 - Numerical diffusion
Section 2.4.4.4.6.4.0 - Basic Writeup - Wikipedia - Numerical diffusion
Section 2.4.4.4.6.4.1 - False diffusion
Section 2.4.4.4.6.5 - Numerical resistivity
Section 2.4.4.4.6.6 - Weak formulation
Section 2.4.4.4.6.7 - Total variation diminishing
Section 2.4.4.4.6.8 - Godunov's theorem
Section 2.4.4.4.6.9 - Motz's problem
Section 2.4.5 - Integral Calculus
Section 2.4.5.1 - Definitions
Section 2.4.5.1.1 - Fundamental theorem of calculus
Section 2.4.5.1.2 - Antiderivative/Indefinite integral
Section 2.4.5.1.3 - Integral
Section 2.4.5.1.4 - Improper Integral
Section 2.4.5.1.5 - Riemann integral
Section 2.4.5.1.6 - Lebesgue integration
Section 2.4.5.1.7 - Contour integration
Section 2.4.5.1.8 - Shell integration
Section 2.4.5.2 - Integration By
Section 2.4.5.2.1 - Parts
Section 2.4.5.2.2 - Discs
Section 2.4.5.2.3 - Cylindrical shells
Section 2.4.5.2.4 - Integration by Substitution
Section 2.4.5.2.4.0 - Basic Writeup - Wikipedia - Integration by Substitution
Section 2.4.5.2.4.1 - Trigonometric Substitution
Section 2.4.5.2.5 - Partial fractions
Section 2.4.5.2.6 - Order of integration
Section 2.4.5.2.7 - Integration by Reduction formulae
Section 2.4.5.2.8 - Inverse chain rule method
Section 2.4.5.3 - Lists of integrals
Section 2.4.5.4- Simplest rules
Section 2.4.5.4.1 - Sum rule in integration
Section 2.4.5.4.2 - Constant factor rule in integration
Section 2.4.5.4.3 - Linearity of integration
Section 2.4.5.4.4 - Trapezium rule
Section 2.4.5.5 - Various kinds of integration
Section 2.4.5.5.1 - Arbitrary constant of integration
Section 2.4.5.5.2 - Integral of the secant function
Section 2.4.5.5.3 - Integral of secant cubed
Section 2.4.5.5.4 - Arclength
Section 2.4.5.6 - Differentiation under the integral sign
Section 2.4.5.7 - Partial fractions in integration
Section 2.4.5.7.0 - Basic Writeup - Wikipedia - Partial fractions in integration
Section 2.4.5.7.1 - Quadratic integral
Section 2.4.5.8 - Proof that 22/7 exceeds π
Section 2.4.5.9 - Numerical Integration(Quadrature)
Section 2.4.5.9.0 - Basic Writeup - Wikipedia - Numerical Integration
Section 2.4.5.9.1 - Rectangle method
Section 2.4.5.9.2 - Trapezoidal rule
Section 2.4.5.9.3 - Simpson's rule
Section 2.4.5.9.3.0 - Basic Writeup - Wikipedia - Simpson's rule
Section 2.4.5.9.3.1 - Adaptive Simpson's method
Section 2.4.5.9.4 - Boole's rule
Section 2.4.5.9.5 - Newton–Cotes formulas
Section 2.4.5.9.6 - Romberg's method
Section 2.4.5.9.7 - Gaussian quadrature
Section 2.4.5.9.7.0 - Gaussian quadrature
Section 2.4.5.9.7.1 - Chebyshev–Gauss quadrature
Section 2.4.5.9.7.2 - Gauss–Hermite quadrature
Section 2.4.5.9.7.3 - Gauss–Jacobi quadrature
Section 2.4.5.9.7.4 - Gauss–Laguerre quadrature
Section 2.4.5.9.7.5 - Gauss–Kronrod quadrature formula
Section 2.4.5.9.7.6 - Gauss–Kronrod rules
Section 2.4.5.9.8 - Tanh-sinh quadrature
Section 2.4.5.9.9 - Clenshaw–Curtis quadrature
Section 2.4.5.9.10 - Adaptive quadrature
Section 2.4.5.9.11 - Monte Carlo integration
Section 2.4.5.9.12 - Quantized state systems method (QSS)
Section 2.4.5.9.13 - Lebedev quadrature
Section 2.4.5.9.14 - Sparse grid
Section 2.4.5.9.15 - Coopmans approximation
Section 2.4.5.9.16 - Numerical differentiation
Section 2.4.5.9.16.0 - Basic Writeup - Wikipedia - Numerical differentiation
Section 2.4.5.9.16.1 - Numerical smoothing and differentiation
Section 2.4.5.9.16.2 - Adjoint state method
Section 2.4.5.9.17 - Euler–Maclaurin formula
Section 2.4.6 - Multivariable Calculus
Section 2.4.6.1 - Formalisms
Section 2.4.6.1.1 - Matrix Calculus
Section 2.4.6.1.2 - Tensor Calculus
Section 2.4.6.1.3 - Exterior Derivative
Section 2.4.6.1.4 - Geometric Calculus
Section 2.4.6.2 - Definitions
Section 2.4.6.2.1 - Partial derivative
Section 2.4.6.2.2 - Multiple integral
Section 2.4.6.2.3 - Line integral
Section 2.4.6.2.4 - Surface integral
Section 2.4.6.2.5 - Volume integral
Section 2.4.6.2.6 - Jacobian Matrix and Determinant (First Order Partial Derivative of a Vector Function)
Section 2.4.6.2.7 - Hessian Matrix (Second Order Partial Derivatives of a Scalar Field)
Section 2.4.6.3 - Disk integration
Section 2.4.6.4 - Gabriel's horn
Section 2.4.6.5 - Curvature
Section 2.4.6.6 - Theorems
Section 2.4.6.6.1 - Green's Theorem
Section 2.4.6.6.2 - Divergence theorem
Section 2.4.6.6.3 - Stokes' theorem
Section 2.4.7 - Stochastic calculus
Section 2.4.7.0 - Basic Writeup - Wikipedia - Stochastic calculus
Section 2.4.7.1 - Itô calculus
Section 2.4.7.2 - Stratonovich integral
Section 2.4.8 - Multiplicative calculus
Section 2.4.9 - Non Standard calculus
Section 2.4.9.0 - Basic Writeup - Wikipedia - Non Standard calculus
Section 2.4.9.1 - Elementary Calculus: An Infinitesimal Approach
Section 2.4.9.2 - Infinitesimal
Section 2.4.9.3 - Archimedes' use of infinitesimals
Section 2.4.10 - Series
Section 2.4.10.0 - Basic Writeup - Wikipedia - Series
Section 2.4.10.1 - Types of Series
Section 2.4.10.1.1 - Infinite series
Section 2.4.10.1.2 - Maclaurin series
Section 2.4.10.1.3 - Taylor series
Section 2.4.10.1.4 - Fourier series
Section 2.4.10.1.5 - Euler–Maclaurin formula
Section 2.4.10.1.6 - Geometric Series
Section 2.4.10.1.7 - Arithmetico-Geometric Sequence
Section 2.4.10.1.8 - Harmonic Series
Section 2.4.10.1.9 - Alternating Series
Section 2.4.10.1.10 - Power Series
Section 2.4.10.1.11 - Binomial Series
Section 2.4.10.1.12 - Taylor Series
Section 2.4.10.2 - Convergence tests
Section 2.4.10.2.0 - Basic Writeup - Wikipedia - Convergence tests
Section 2.4.10.2.1 - Summand limit (term test)
Section 2.4.10.2.2 - Ratio Test
Section 2.4.10.2.3 - Root Test
Section 2.4.10.2.4 - Integral Test for Convergence
Section 2.4.10.2.5 - Direct comparison Test
Section 2.4.10.2.6 - Limit comparison Test
Section 2.4.10.2.7 - Alternating series Test
Section 2.4.10.2.8 - Cauchy condensation Test
Section 2.4.10.2.9 - Dirichlet Test
Section 2.4.10.2.10 - Abel Test
Section 2.4.11 - Vector Calculus
Section 2.4.11.0 - Basic Writeup - Wikipedia - Vector Calculus
Section 2.4.11.1 - Gradient (Multi-variable Generalization of Vector Derivative)
Section 2.4.11.2 - Divergence Operator
Section 2.4.11.3 - Curl Operator
Section 2.4.11.4 - Laplacian Operator
Section 2.4.11.5 - Directional derivative
Section 2.4.11.6 - Vector Calculus Identities
Section 2.4.11.7 - Theorems
Section 2.4.11.7.1 - Divergence Theorem
Section 2.4.11.7.2 - Gradient Theorem
Section 2.4.11.7.3 - Green's Theorem
Section 2.4.11.7.4 - Kelvin–Stokes Theorem
Section 2.4.11.7.5 - Stokes Theorem
Section 2.6.1 - Information Theory
Section 2.6.1.0 - Introductory Writeups
Section 2.6.1.0.1 - Basic Writeup - Wikipedia - Information Theory
Section 2.6.1.0.2 - Detailed Writeup - Gray - Entropy and Information Theory
Section 2.6.1.0.3 - Video - Mathematical Monk - Information Theory
Section 2.6.1.1 - Entropy
Section 2.6.1.2 - Differential Entropy
Section 2.6.1.3 - Conditional entropy
Section 2.6.1.4 - Joint entropy
Section 2.6.1.5 - Mutual information
Section 2.6.1.6 - Conditional mutual information
Section 2.6.1.7 - Relative entropy
Section 2.6.1.8 - Entropy rate
Section 2.6.1.9 - Asymptotic equipartition property
Section 2.6.1.10 - Rate–distortion theory
Section 2.6.1.11 - Shannon's source coding theorem
Section 2.6.1.12 - Channel capacity
Section 2.6.1.13 - Noisy-channel coding theorem
Section 2.6.1.14 - Shannon–Hartley theorem
Section 2.6.1.15 - Quantities of information
Section 2.6.1.15.1 - Entropy of an information source
Section 2.6.1.15.2 - Joint entropy
Section 2.6.1.15.3 - Conditional entropy (equivocation)
Section 2.6.1.15.4 - Mutual information (transinformation)
Section 2.6.1.15.5 - Kullback–Leibler divergence (information gain)
Section 2.6.1.15.6 - Rényi entropy
Section 2.6.1.15.7 - Differential entropy
Section 2.6.1.15.8 - Conditional mutual information.
Section 2.6.1.16 - Concepts
Section 2.6.1.16 - Ban (Unit)
Section 2.6.1.16.2 - Channel capacity
Section 2.6.1.16.3 - Communication channel
Section 2.6.1.16.4 - Communication source
Section 2.6.1.16.5 - Conditional entropy
Section 2.6.1.16.6 - Covert channel
Section 2.6.1.16.7 - Decoder
Section 2.6.1.16.8 - Differential entropy
Section 2.6.1.16.9 - Encoder
Section 2.6.1.16.10 - Fungible information
Section 2.6.1.16.11 - Information entropy
Section 2.6.1.16.12 - Joint entropy
Section 2.6.1.16.13 - Kullback–Leibler divergence
Section 2.6.1.16.14 - Mutual information
Section 2.6.1.16.15 - Pointwise mutual information (PMI)
Section 2.6.1.16.16 - Receiver (information theory)
Section 2.6.1.16.17 - Redundancy
Section 2.6.1.16.18 - Rényi entropy
Section 2.6.1.16.19 - Self-information
Section 2.6.1.16.20 - Unicity distance
Section 2.6.1.16.21 - Variety
Section 2.6.1.16.22 - Hamming distance
Section 2.6.1.17 - Theory
Section 2.6.1.17.1 - Coding theory
Section 2.6.1.17.2 - Detection theory
Section 2.6.1.17.3 - Estimation theory
Section 2.6.1.17.4 - Fisher information
Section 2.6.1.17.5 - Information algebra
Section 2.6.1.17.6 - Information asymmetry
Section 2.6.1.17.7 - Information field theory
Section 2.6.1.17.8 - Information geometry
Section 2.6.1.17.9 - Information theory and measure theory
Section 2.6.1.17.10 - Kolmogorov complexity
Section 2.6.1.17.11 - List of unsolved problems in information theory
Section 2.6.1.17.12 - Logic of information
Section 2.6.1.17.13 - Network coding
Section 2.6.1.17.14 - Philosophy of information
Section 2.6.1.17.15 - Quantum information science
Section 2.6.1.17.16 - Source coding
Section 2.6.2 - Information Retrieval
Section 2.6.2.0 - Basic Writeup - Wikipedia - Information Retrieval
Section 2.6.2.1 - Model Types
Section 2.6.2.1.0 - Introductory Writeups
Section 2.6.2.1.0.1 - Detailed Writeups
Section 2.6.2.1.0.1.1 - Part 1 - Furh - Models in Information Retrieval
Section 2.6.2.1.0.1.2 - Part 2 - Chen - Models for Information Retrieval
Section 2.6.2.1.1 - First (and Second) Dimensions
Section 2.6.2.1.1.0 - Basic Writeup - Wikipedia - First Dimension: Mathematical Basis
Section 2.6.2.1.1.1 - First Dimension: Set-theoretic models
Section 2.6.2.1.1.1.0 - Basic Writeup - Slide Player - Set-theoretic models
Section 2.6.2.1.1.1.1 - Second Dimension: Without Term Interdependencies
Section 2.6.2.1.1.1.1.1 - Standard Boolean model
Section 2.6.2.1.1.1.1.2 - Extended Boolean model
Section 2.6.2.1.1.1.2 - Second Dimension: With Transcendant Term Interdependencies
Section 2.6.2.1.1.1.2.1 - Fuzzy retrieval
Section 2.6.2.1.1.2 - First Dimension: Algebraic models
Section 2.6.2.1.1.2.0 - Basic Writeup - Pannu,James,Bird - Comparison of Information Retrieval Models: Algebraic models
Section 2.6.2.1.1.2.1 - Second Dimension: Without Term Interdependencies
Section 2.6.2.1.1.2.1.1 - Vector space model
Section 2.6.2.1.1.2.1.2 - Extended Boolean model
Section 2.6.2.1.1.2.2 - Second Dimension: With Imminent Term Interdependencies
Section 2.6.2.1.1.2.2.1 - Generalized vector space model
Section 2.6.2.1.1.2.2.2 - Latent semantic indexing
Section 2.6.2.1.1.2.2.3 - Latent semantic analysis
Section 2.6.2.1.1.2.2.4 - Spread Activation Neuronal Network
Section 2.6.2.1.1.2.3 - Second Dimension: With Transcendant Term Interdependencies
Section 2.6.2.1.1.2.3.1 - Topic-based (Enhanced) Vector Space Model
Section 2.6.2.1.1.2.3.2 - Feedforward Neural Networks
Section 2.6.2.1.1.3 - First Dimension: Probabilistic models
Section 2.6.2.1.1.3.0 - Basic Writeup - Stanford - Probabilistic Information Retrieval
Section 2.6.2.1.1.3.1 - Second Dimension: Without Term Interdependencies
Section 2.6.2.1.1.3.1.1 - Binary Independence Model
Section 2.6.2.1.1.3.1.2 - Language models
Section 2.6.2.1.1.3.1.3 - Inference Network
Section 2.6.2.1.1.3.1.4 - Bayesian Network
Section 2.6.2.1.1.3.1.5 - Probabilistic relevance model
Section 2.6.2.1.1.3.1.5.0 - Basic Writeup - Probabilistic relevance model
Section 2.6.2.1.1.3.1.5.1 - Okapi (BM25)
Section 2.6.2.1.1.3.1.6 - Uncertain inference
Section 2.6.2.1.1.3.2 - Second Dimension: With Term Interdependencies
Section 2.6.2.1.1.3.2.1 - Divergence-from-randomness model
Section 2.6.2.1.1.3.2.2 - Latent Dirichlet allocation
Section 2.6.2.1.1.4 - First Dimension: Feature-based (Learning to Rank) retrieval models
Section 2.6.2.2 - Evaluation Metrics
Section 2.6.2.2.0 - Basic Writeup - Wikipedia - Evaluation Metrics
Section 2.6.2.2.1 - Online metrics
Section 2.6.2.2.1.1 - Session abandonment rate
Section 2.6.2.2.1.2 - Click-through rate
Section 2.6.2.2.1.3 - Session success rate
Section 2.6.2.2.1.4 - Zero result rate
Section 2.6.2.2.2 - Offline metrics
Section 2.6.2.2.2.1 - Precision and Recall
Section 2.6.2.2.2.2 - Fall-out
Section 2.6.2.2.2.3 - F-score / F-measure
Section 2.6.2.2.2.4 - Average precision
Section 2.6.2.2.2.5 - Precision at K
Section 2.6.2.2.2.6 - R-Precision
Section 2.6.2.2.2.7 - Mean average precision
Section 2.6.2.2.2.8 - Discounted cumulative gain
Section 2.6.2.2.2.9 - Mean reciprocal rank
Section 2.6.2.2.2.10 - Spearman's rank correlation coefficient
Section 2.6.2.2.2.11 - bpref
Section 2.6.2.2.2.12 - GMAP - geometric mean of (per-topic) average precision
Section 2.6.2.2.2.13 - Maximal Marginal Relevance (MMR)
Section 2.6.2.2.2.14 - Measures of both relevance and credibility (for fake news in search results)
Section 2.6.2.2.2.15 - Sensitivity
Section 2.6.2.2.2.16 - Specificity
Section 2.6.2.2.2.17 - Positive Predictive Value
Section 2.6.2.2.2.18 - Negative Predictive Value
Section 2.6.2.2.2.19 - Type 1 and Type 2 Errors
Section 2.6.2.2.2.20 - False Discovery Rate
Section 2.6.2.2.2.21 - False Omission Rate
Section 2.6.2.2.2.22 - Accuracy
Section 2.6.2.2.2.23 - Matthews Corellation Coefficient
Section 2.6.2.2.2.24 - Informedness
Section 2.6.2.2.2.25 - Visualization
Section 2.6.2.2.2.16.1 - Graphs which chart precision on one axis and recall on the other
Section 2.6.2.2.2.25.2 - Histograms of average precision over various topics
Section 2.6.2.2.2.25.3 - Receiver operating characteristic (ROC curve)
Section 2.6.2.2.2.25.4 - Confusion (Error) matrix
Section 2.6.2.3 - Other Topics
Section 2.6.2.3.1 - Adversarial information retrieval
Section 2.6.2.3.2 - Collaborative information seeking
Section 2.6.2.3.3 - Controlled vocabulary
Section 2.6.2.3.4 - Cross-language information retrieval
Section 2.6.2.3.5 - Data mining
Section 2.6.2.3.6 - Human–computer information retrieval (HCIR)
Section 2.6.2.3.7 - Information extraction
Section 2.6.2.3.8 - Knowledge visualization
Section 2.6.2.3.9 - Multimedia information retrieval
Section 2.6.2.3.10 - Personal information management
Section 2.6.2.3.11 - Relevance (information retrieval)
Section 2.6.2.3.12 - Relevance feedback
Section 2.6.2.3.13 - Rocchio classification
Section 2.6.2.3.14 - Search index
Section 2.6.2.3.15 - Social information seeking
Section 2.6.2.3.16 - Subject indexing
Section 2.6.2.3.17 - Temporal information retrieval
Section 2.6.2.3.18 - tf-idf
Section 2.6.2.3.19 - XML retrieval
Section 2.6.2.3.20 - Web mining
Section 2.7.1 - Optimization
Section 2.7.1.0 - Basic Writeup
Section 2.7.1.0.1 - Part 1 - Katariya - Introduction to Optimization
Section 2.7.1.0.2 - Part 2 - Katariya - Local vs Global Optimization
Section 2.7.1.1 - Basic Concepts
Section 2.7.1.1.1 - Active set
Section 2.7.1.1.2 - Candidate solution
Section 2.7.1.1.3 - Constraint (mathematics)
Section 2.7.1.1.3.0 - Basic Writeup - Wikipedia - Constraint (mathematics)
Section 2.7.1.1.3.1 - Constrained optimization
Section 2.7.1.1.3.2 - Binary constraint
Section 2.7.1.1.4 - Corner solution
Section 2.7.1.1.5 - Feasible region
Section 2.7.1.1.6 - Global optimum
Section 2.7.1.1.7 - Local optimum
Section 2.7.1.1.8 - Maxima and minima
Section 2.7.1.1.9 - Slack variable
Section 2.7.1.1.10 - Continuous optimization
Section 2.7.1.1.11 - Discrete optimization
Section 2.7.1.2 - Major Sub Fields
Section 2.7.1.2.1 - Single Objective Optimization
Section 2.7.1.2.1.0 - Basic Writeup - Wikipedia - Mathematical Optimization SubFields
Section 2.7.1.2.1.1 - Convex Optimization
Section 2.7.1.2.1.1.0 - Basic Writeup - Wikipedia - Convex Optimization
Section 2.7.1.2.1.1.1 - Complexity Theory in Convex Optimization
Section 2.7.1.2.1.1.2 - Convex Optimization Techniques
Section 2.7.1.2.1.1.2.1 - Linear programming (LP)
Section 2.7.1.2.1.1.2.2 - Conic Optimization
Section 2.7.1.2.1.1.2.2.0 - Basic Writeup - Wikipedia - Conic Optimization
Section 2.7.1.2.1.1.2.2.1 - Second Order Cone Programming ( SOCP )
Section 2.7.1.2.1.1.2.2.2 - Semi definite programming (SDP)
Section 2.7.1.2.1.1.2.2.3 - Sum of Squares Optimization
Section 2.7.1.2.1.1.2.2.4 - Quadratic Programming
Section 2.7.1.2.1.1.2.2.5 - Quadratically Constrained Quadratic Programming
Section 2.7.1.2.1.1.2.2.6 - Convex Quadratic Minimization with Linear Constraints
Section 2.7.1.2.1.1.2.5 - Geometric programming
Section 2.7.1.2.1.1.2.6 - Entropy maximization with Appropriate Constraints
Section 2.7.1.2.1.1.2.7 - Basis pursuit
Section 2.7.1.2.1.1.2.7.0 - Basic Writeup - Wikipedia - Basis pursuit
Section 2.7.1.2.1.1.2.7.1 - Basis pursuit denoising (BPDN)
Section 2.7.1.2.1.1.2.7.1.0 - Basic Writeup - Wikipedia - Basis pursuit denoising (BPDN)
Section 2.7.1.2.1.1.2.7.1.1 - In-crowd algorithm
Section 2.7.1.2.1.1.2.8 - Linear matrix inequality
Section 2.7.1.2.1.1.2.9 - Bregman method
Section 2.7.1.2.1.1.2.10 - Proximal gradient method
Section 2.7.1.2.1.1.2.11 - Subgradient method
Section 2.7.1.2.1.1.2.12 - Biconvex optimization
Section 2.7.1.2.1.1.3 - Convex Optimization Classes of Methods
Section 2.7.1.2.1.1.3.1 - Bundle Methods
Section 2.7.1.2.1.1.3.2 - Sub-Gradient Projections
Section 2.7.1.2.1.1.3.3 - Interior Point Methods
Section 2.7.1.2.1.1.3.4 - Cutting Plane Methods
Section 2.7.1.2.1.1.3.5 - Ellipsoid Method
Section 2.7.1.2.1.1.3.6 - Subgradient Method
Section 2.7.1.2.1.1.3.7 - Dual Subgradient Drift Plus Penalty Method
Section 2.7.1.2.1.2 - Linear Programming (Optimization)
Section 2.7.1.2.1.2.0 - Basic Writeup - Wikipedia - Linear Programming (Optimization)
Section 2.7.1.2.1.2.1 - Integer Programming (Optimization)
Section 2.7.1.2.1.2.2 - Algorithms for linear programming
Section 2.7.1.2.1.2.2.1 - Simplex algorithm
Section 2.7.1.2.1.2.2.1.0 - Basic Writeup - Wikipedia - Simplex algorithm
Section 2.7.1.2.1.2.2.1.1 - Bland's rule
Section 2.7.1.2.1.2.2.1.2 - Klee–Minty cube
Section 2.7.1.2.1.2.2.1.3 - Criss-cross algorithm
Section 2.7.1.2.1.2.2.1.4 - Big M method
Section 2.7.1.2.1.2.2.2 - Interior point method
Section 2.7.1.2.1.2.2.2.0 - Basic Writeup - Wikipedia - Interior point method
Section 2.7.1.2.1.2.2.2.1 - Ellipsoid method
Section 2.7.1.2.1.2.2.2.2 - Karmarkar's algorithm
Section 2.7.1.2.1.2.2.2.3 - Mehrotra predictor–corrector method
Section 2.7.1.2.1.2.2.3 - Column generation
Section 2.7.1.2.1.2.2.4 - k-approximation of k-hitting set
Section 2.7.1.2.1.2.3 - Linear complementarity problem
Section 2.7.1.2.1.2.4 - Decompositions
Section 2.7.1.2.1.2.4.1 - Benders' decomposition
Section 2.7.1.2.1.2.4.2 - Dantzig–Wolfe decomposition
Section 2.7.1.2.1.2.4.3 - Theory of two-level planning
Section 2.7.1.2.1.2.4.4 - Variable splitting
Section 2.7.1.2.1.2.5 - Basic solution (linear programming)
Section 2.7.1.2.1.2.6 - Fourier–Motzkin elimination
Section 2.7.1.2.1.2.7 - Hilbert basis (linear programming)
Section 2.7.1.2.1.2.8 - LP-type problem
Section 2.7.1.2.1.2.9 - Linear inequality
Section 2.7.1.2.1.2.10 - Vertex enumeration problem
Section 2.7.1.2.1.3 - Quadratic programming
Section 2.7.1.2.1.3.0 - Basic Writeup - Wikipedia - Quadratic programming
Section 2.7.1.2.1.3.1 - Linear least squares (mathematics)
Section 2.7.1.2.1.3.2 - Total least squares
Section 2.7.1.2.1.3.3 - Frank–Wolfe algorithm
Section 2.7.1.2.1.3.4 - Sequential minimal optimization
Section 2.7.1.2.1.3.5 - Bilinear program
Section 2.7.1.2.1.4 - Fractional programming
Section 2.7.1.2.1.5 - Non-Linear programming
Section 2.7.1.2.1.5.0 - Basic Writeup - Wikipedia - Non-Linear programming
Section 2.7.1.2.1.5.1 - Special cases of nonlinear programming
Section 2.7.1.2.1.5.1.1 - Linear programming
Section 2.7.1.2.1.5.1.2 - Convex optimization
Section 2.7.1.2.1.5.1.3 - Geometric programming
Section 2.7.1.2.1.5.1.3.0 - Basic Writeup - Wikipedia - Geometric programming
Section 2.7.1.2.1.5.1.3.1 - Signomial
Section 2.7.1.2.1.5.1.3.2 - Posynomial
Section 2.7.1.2.1.5.1.4 - Quadratically constrained quadratic program
Section 2.7.1.2.1.5.1.5 - Linear-fractional programming
Section 2.7.1.2.1.5.1.5.0 - Basic Writeup - Wikipedia - Linear-fractional programming
Section 2.7.1.2.1.5.1.5.1 - Fractional programming
Section 2.7.1.2.1.5.1.6 - Nonlinear complementarity problem (NCP)
Section 2.7.1.2.1.5.1.7 - Least squares
Section 2.7.1.2.1.5.1.7.0 - Basic Writeup - Wikipedia - Least squares
Section 2.7.1.2.1.5.1.7.1 - Non-linear least squares
Section 2.7.1.2.1.5.1.7.2 - Gauss–Newton algorithm
Section 2.7.1.2.1.5.1.7.2.0 - Basic Writeup - Wikipedia - Gauss–Newton algorithm
Section 2.7.1.2.1.5.1.7.2.1 - BHHH algorithm
Section 2.7.1.2.1.5.1.7.2.2 - Generalized Gauss–Newton method
Section 2.7.1.2.1.5.1.7.3 - Levenberg–Marquardt algorithm
Section 2.7.1.2.1.5.1.7.4 - Iteratively reweighted least squares (IRLS)
Section 2.7.1.2.1.5.1.7.5 - Partial least squares
Section 2.7.1.2.1.5.1.7.5.0 - Basic Writeup - Wikipedia - Partial least squares
Section 2.7.1.2.1.5.1.7.5.1 - Non-linear iterative partial least squares (NIPLS)
Section 2.7.1.2.1.5.1.8 - Mathematical programming with equilibrium constraints
Section 2.7.1.2.1.5.1.9 - Univariate optimization
Section 2.7.1.2.1.5.1.9.1 - Golden section search
Section 2.7.1.2.1.5.1.9.2 - Successive parabolic interpolation
Section 2.7.1.2.1.5.2 - General algorithms
Section 2.7.1.2.1.5.2.1 - Concepts
Section 2.7.1.2.1.5.2.1.1 - Descent direction
Section 2.7.1.2.1.5.2.1.2 - Guess value
Section 2.7.1.2.1.5.2.1.3 - Line search
Section 2.7.1.2.1.5.2.1.3.0 - Basic Writeup - Wikipedia - Line search
Section 2.7.1.2.1.5.2.1.3.1 - Backtracking line search
Section 2.7.1.2.1.5.2.1.3.2 - Wolfe conditions
Section 2.7.1.2.1.5.2.2 - Gradient methods
Section 2.7.1.2.1.5.2.2.0 - Basic Writeup - Wikipedia - Gradient method
Section 2.7.1.2.1.5.2.2.1 - Gradient descent
Section 2.7.1.2.1.5.2.2.1.0 - Basic Writeup - Wikipedia - Gradient descent
Section 2.7.1.2.1.5.2.2.1.1 - Stochastic gradient descent
Section 2.7.1.2.1.5.2.2.2 - Landweber iteration
Section 2.7.1.2.1.5.2.3 - Successive linear programming (SLP)
Section 2.7.1.2.1.5.2.4 - Sequential quadratic programming (SQP)
Section 2.7.1.2.1.5.2.5 - Newton's method in optimization
Section 2.7.1.2.1.5.2.5.0 - Basic Writeup - Wikipedia - Newton's method in optimization
Section 2.7.1.2.1.5.2.5.1 - Kantorovich theorem
Section 2.7.1.2.1.5.2.5.2 - Newton fractal
Section 2.7.1.2.1.5.2.5.3 - Quasi-Newton method
Section 2.7.1.2.1.5.2.5.3.0 - Basic Writeup - Wikipedia - Quasi-Newton method
Section 2.7.1.2.1.5.2.5.3.1 - Broyden's method
Section 2.7.1.2.1.5.2.5.3.2 - Symmetric rank-one
Section 2.7.1.2.1.5.2.5.3.3 - Davidon–Fletcher–Powell formula
Section 2.7.1.2.1.5.2.5.3.4 - Broyden–Fletcher–Goldfarb–Shanno algorithm
Section 2.7.1.2.1.5.2.5.3.5 - Limited-memory BFGS method
Section 2.7.1.2.1.5.2.5.4 - Steffensen's method
Section 2.7.1.2.1.5.2.6 - Nonlinear conjugate gradient method
Section 2.7.1.2.1.5.2.7 - Derivative-free methods
Section 2.7.1.2.1.5.2.7.1 - Coordinate descent
Section 2.7.1.2.1.5.2.7.1.0 - Basic Writeup - Wikipedia - Coordinate descent
Section 2.7.1.2.1.5.2.7.1.1 - Adaptive coordinate descent
Section 2.7.1.2.1.5.2.7.1.2 - Random coordinate descent
Section 2.7.1.2.1.5.2.7.2 - Nelder–Mead method
Section 2.7.1.2.1.5.2.7.3 - Pattern search (optimization)
Section 2.7.1.2.1.5.2.7.4 - Powell's method
Section 2.7.1.2.1.5.2.7.5 - Rosenbrock methods
Section 2.7.1.2.1.5.2.8 - Augmented Lagrangian method
Section 2.7.1.2.1.5.2.9 - Ternary search
Section 2.7.1.2.1.5.2.10 - Tabu search
Section 2.7.1.2.1.5.2.11 - Guided Local Search
Section 2.7.1.2.1.5.2.12 - Reactive search optimization (RSO)
Section 2.7.1.2.1.5.2.13 - MM algorithm — majorize-minimization
Section 2.7.1.2.1.5.2.14 - Least absolute deviations
Section 2.7.1.2.1.5.2.14.0 - Basic Writeup - Wikipedia - Least absolute deviations
Section 2.7.1.2.1.5.2.14.1 - Expectation–maximization algorithm
Section 2.7.1.2.1.5.2.14.1.0 - Basic Writeup - Wikipedia - Expectation–maximization algorithm
Section 2.7.1.2.1.5.2.14.1.1 - Ordered subset expectation maximization
Section 2.7.1.2.1.5.2.15 - Nearest neighbor search
Section 2.7.1.2.1.5.2.16 - Space mapping
Section 2.7.1.2.1.6 - Stochastic programming
Section 2.7.1.2.1.7 - Robust Optimization
Section 2.7.1.2.1.8 - Combinatorial Optimization
Section 2.7.1.2.1.9 - Stochastic Optimization
Section 2.7.1.2.1.10 - Infinite-dimensional Optimization
Section 2.7.1.2.1.11 - Heuristics Optimization
Section 2.7.1.2.1.12 - Meta Heuristics Optimization(See Section 4.11.1.1 - Evolutionary Algorithms)
Section 2.7.1.2.1.13 - Constraints Programming
Section 2.7.1.2.1.14 - Disjunctive programming
Section 2.7.1.2.1.15 - Space mapping
Section 2.7.1.2.2 - Multi-Objective Optimization
Section 2.7.1.2.2.0 - Introductory Writeups
Section 2.7.1.2.2.0.1 - Basic Writeup - Wikipedia - Multi-Objective Optimization
Section 2.7.1.2.2.0.2 - Detailed Writeup - Wikipedia - Multi-Objective Optimization
Section 2.7.1.2.2.1 - No Preference Methods
Section 2.7.1.2.2.1.0 - Basic Writeup - Miettinen - Introduction to MultiObjective Optimization: NonInteractive Approaches
Section 2.7.1.2.2.1.1 - Method of Global Criterion
Section 2.7.1.2.2.1.2 - Neutral Compromise Solution
Section 2.7.1.2.2.2 - A-Priori Methods
Section 2.7.1.2.2.2.0 - Basic Writeup - Meittinen - Introduction to MultiObjective Optimization: NonInteractive Approaches
Section 2.7.1.2.2.2.1 - Value Function Method
Section 2.7.1.2.2.2.2 - Lexicographic Ordering
Section 2.7.1.2.2.2.3 - Goal Programming
Section 2.7.1.2.2.3 - A Posteriori Methods
Section 2.7.1.2.2.3.0 - Basic Writeup - Wikipedia - MultiObjective Optimization: A Posteriori Methods
Section 2.7.1.2.2.3.1 - Normal Boundary Intersection (NBI)
Section 2.7.1.2.2.3.2 - Modified Normal Boundary Intersection (NBIm)
Section 2.7.1.2.2.3.3 - Genetic Algorithm Based Normal Boundary Intersection (GANBI)
Section 2.7.1.2.2.3.4 - Normal Constaint (NC)
Section 2.7.1.2.2.3.5 - Successive Pareto Optimization (SPO)
Section 2.7.1.2.2.3.6 - Directed Search Domain
Section 2.7.1.2.2.3.7 - NSGA-II
Section 2.7.1.2.2.3.8 - Pareto Surface Generation (PGEN)
Section 2.7.1.2.2.3.9 - Indirect Optimization on the basis of Self-Organization (IOSO)
Section 2.7.1.2.2.3.10 - S-Metric Selection Evolutionary Multi-Objective Algorithm (SMS-EMOA)
Section 2.7.1.2.2.3.11 - Approximation Guided Evolution
Section 2.7.1.2.2.3.12 - Reactive Search Optimization
Section 2.7.1.2.2.3.13 - Benson's Algorithm
Section 2.7.1.2.2.3.14 - Multi-Objective Particle Swarm Optimization (MOPSO)
Section 2.7.1.2.2.3.15 - Subpopulation Algorithm Based on Novelty
Section 2.7.1.2.2.4 - Interactive Methods
Section 2.7.1.2.2.4.0 - Basic Writeup - Mietten,Ruiz,Wierzibicki - Introduction to MultiObjective Optimization: Interactive Approaches
Section 2.7.1.2.2.4.1 - Trade Off Methods
Section 2.7.1.2.2.4.1.1 - Zionts and Wallenius Method (ZW Method)
Section 2.7.1.2.2.4.1.2 - Interactive Surrogate Worth Trade-off Method (ISWT)
Section 2.7.1.2.2.4.1.3 - Interactive Geoffrion, Dyer and Feinberg (GDF)
Section 2.7.1.2.2.4.1.4 - Sequential Proxy Optimization Technique (SPOT)
Section 2.7.1.2.2.4.1.5 - Gradient Based Interactive Step Trade-off Method(GRIST)
Section 2.7.1.2.2.4.2 - Reference Point Approaches
Section 2.7.1.2.2.4.3 - Classification-Based Methods
Section 2.7.1.2.2.4.3.0 - Basic Writeup - Mietten,Ruiz,Wierzibicki - Introduction to MultiObjective Optimization: Interactive Approaches
Section 2.7.1.2.2.4.3.1 - Step Method (STEM)
Section 2.7.1.2.2.4.3.2 - Satisficing Trade-off Method (STOM)
Section 2.7.1.2.2.4.3.3 - Nimbus Method
Section 2.7.1.2.2.4.3.4 - Interactive Reference Direction Algorithm
Section 2.7.1.2.2.4.3.5 - Interactive decision making approach (NIDMA)
Section 2.7.1.2.2.5 - Hybrid Methods
Section 2.7.1.2.2.5.0 - Basic Writeup - Goel,Deb - Hybrid Methods for Multi-Objective Evolutionary Algorithms
Section 2.7.1.2.2.5.1 - Posteriori Approach
Section 2.7.1.2.2.5.2 - Online Approach
Section 2.7.1.2.3 - Evolutionary Multimodal Optimization
Section 2.7.1.3 - Common Local and Global Computational Optimization Techniques
Section 2.7.1.3.0 - Introductory Writeups
Section 2.7.1.3.0.1 - Basic Writeup - Wikipedia - Mathematical Optimization: Computational Optimization Techniques
Section 2.7.1.3.0.2 - Detailed Writeup - Text Book - Yang - Computational Optimization, Methods and Algorithms
Section 2.7.1.3.1 - Optimization algorithms
Section 2.7.1.3.2 - Iterative Methods
Section 2.7.1.3.2.0 - Basic Writeup
Section 2.7.1.3.2.1 - Hessian Iterative Methods in Optimizations
Section 2.7.1.3.2.1.0 - Basic Writeup - Wikipedia - Hessian Matrix: Use in Optimization
Section 2.7.1.3.2.1.1 - Newtons's Method
Section 2.7.1.3.2.1.2 - Sequential Quadratic Programming
Section 2.7.1.3.2.1.3 - Interior Point Method
Section 2.7.1.3.2.2 - Gradient, Approximate Gradient and Sub-Gradient Methods
Section 2.7.1.3.2.2.1 - Coordinate Descent Methods
Section 2.7.1.3.2.2.2 - Conjugate gradient methods
Section 2.7.1.3.2.2.3 - Gradient Descent
Section 2.7.1.3.2.2.3.1 - Introductory Writeups
Section 2.7.1.3.2.2.3.1.1 - Detailed Writeups
Section 2.7.1.3.2.2.3.1.1.1 - Detailed Writeup - Ruder - Optimizing Gradient Descent
Section 2.7.1.3.2.2.3.1.1.2 - Detailed Writeup - Wikipedia - Gradient Descent
Section 2.7.1.3.2.2.3.2 - Visualizing and Animating Optimization Algorithms with Matplotlib
Section 2.7.1.3.2.2.3.3 - Batch Gradient Descent
Section 2.7.1.3.2.2.3.4 - Stochastic Gradient Descent (SGD)
Section 2.7.1.3.2.2.3.4.0 - Basic Writeup - Wikipedia - Stochastic Gradient Descent
Section 2.7.1.3.2.2.3.4.1 - Accelerated Gradient Descent
Section 2.7.1.3.2.2.3.4.2 - Nesterov Accelerated Gradient Descent
Section 2.7.1.3.2.2.3.4.3 - Adaptive Gradient Descent (AdaGrad)
Section 2.7.1.3.2.2.3.4.4 - Adaptive Delta (AdaDelta)
Section 2.7.1.3.2.2.3.4.5 - Root Mean Square Prop (RMS Prop)
Section 2.7.1.3.2.2.3.4.6 - Adaptive Moment Estimation (Adam)
Section 2.7.1.3.2.2.3.4.6.0 - Basic Writeup - Ruder - Optimizing Gradient Descent: Adam
Section 2.7.1.3.2.2.3.4.6.1 - Nesterov Adam (Nadam)
Section 2.7.1.3.2.2.3.4.6.2 - Adaptive Moment Maximization
Section 2.7.1.3.2.2.3.4.7 - Kalman Based Stochastic Gradient Descent (kSGD)
Section 2.7.1.3.2.2.4 - Subgradient Methods
Section 2.7.1.3.2.2.5 - Bundle Method Of Descent
Section 2.7.1.3.2.2.6 - Ellipsoid Method
Section 2.7.1.3.2.2.7 - Reduced gradient method (Frank–Wolfe)
Section 2.7.1.3.2.2.8 - Quasi-Newton Methods
Section 2.7.1.3.2.2.8.0 - Basic Writeup - Wikipedia - Quasi-Newton Method
Section 2.7.1.3.2.2.8.1 - Broyden-Fletcher-Goldfarb-Shanno (BFGS)
Section 2.7.1.3.2.2.8.2 - L-BFGS (Using Limited Computer Memory)
Section 2.7.1.3.2.2.9 - Simultaneous Perturbation Stochastic Approximation (SPSA)
Section 2.7.1.3.2.2.10 - Proximal Gradient Methods
Section 2.7.1.3.3 - Global Optimization
Section 2.7.1.3.3.0 - Basic Writeup - Wikipedia - Global Optmization
Section 2.7.1.3.3.1 - Deterministic Methods
Section 2.7.1.3.3.1.0 - Introductory Writeups
Section 2.7.1.3.3.1.0.1 - Basic Writeup - Wikipedia - Deterministic Global Optimization
Section 2.7.1.3.3.1.0.2 - Detailed Writeup - Floudas - Deterministic Global Optimization: Advances in Theory and Applications
Section 2.7.1.3.3.1.1 - Inner-Outer Approximation
Section 2.7.1.3.3.1.2 - Cutting Plane Methods
Section 2.7.1.3.3.1.3 - Branch and Bound Method
Section 2.7.1.3.4.1.4 Interval Arithmetic Method
Section 2.7.1.3.5.1.5 Methods based on Real Algebraic Geometry
Section 2.7.1.3.3.2 - Stochastic Methods
Section 2.7.1.3.3.2.0 - Basic Writeup - Wikipedia - Stochastic Optimization
Section 2.7.1.3.3.2.1 - Direct Monte-Carlo Sampling
Section 2.7.1.3.3.2.2 - Stochastic Tunneling (STUN)
Section 2.7.1.3.3.2.3 - Parallel Tempering
Section 2.7.1.3.3.3 - Heuristic and Meta-Heuristic Methods
Section 2.7.1.3.3.3.0 - Basic Writeup - Wikipedia - Metaheuristic Methods
Section 2.7.1.3.3.3.1 - Simulated Annealing
Section 2.7.1.3.3.3.2 - Tabu Search
Section 2.7.1.3.3.3.3 - Evolutionary Algorithms
Section 2.7.1.3.3.3.4 - Differential Evolution
Section 2.7.1.3.3.3.5 - Swarm-Based Optimization Algorithms
Section 2.7.1.3.3.3.5.0 - Basic Writeup - Wikipedia - Swarm Intelligence
Section 2.7.1.3.3.3.5.1 - Particle Swarm Optimization
Section 2.7.1.3.3.3.5.2 - Social Cognitive Optimization
Section 2.7.1.3.3.3.5.3 - Multi-swarm Optimization
Section 2.7.1.3.3.3.5.4 - Ant Colony Optimization
Section 2.7.1.3.3.3.6 - Memetic Algorithms
Section 2.7.1.3.3.3.7 - Graduated Optimization
Section 2.7.1.3.3.3.8 - Reactive Search Optimization
Section 2.7.1.4 Objective Functions
Section 2.7.1.4.1 - Loss Functions
Section 2.7.1.4.1.0 - Basic Writeup - Wikipedia - Loss Function
Section 2.7.1.4.1.1 - Regret Loss Functions
Section 2.7.1.4.1.2 - Quadratic Loss Functions
Section 2.7.1.4.1.3 - Common Machine Learning Loss Functions
Section 2.7.1.4.1.3.0 - Basic Writeup - Prince Grover - 5 Regression Loss Functions All Machine Learners Should Know
Section 2.7.1.4.1.3.1 - Regression Loss Functions
Section 2.7.1.4.1.3.1.1 - Mean Squared Error / Quadratic Error / L2 Loss
Section 2.7.1.4.1.3.1.2 - Root Mean Squared Error
Section 2.7.1.4.1.3.1.3 - Mean Absolute Error
Section 2.7.1.4.1.3.1.4 - Mean Absolute Percentage Error
Section 2.7.1.4.1.3.1.5 - Mean Squared Logarithmic Error Loss
Section 2.7.1.4.1.3.1.6 - Huber Loss / Smooth Mean Absolute Error Loss
Section 2.7.1.4.1.3.1.7 - Log cosh Loss
Section 2.7.1.4.1.3.1.8 - Quantile Loss (Loss in Quantile Regression)
Section 2.7.1.4.1.3.2 - Classification Loss Functions
Section 2.7.1.4.1.3.2.1 - Square Loss
Section 2.7.1.4.1.3.2.2 - Hinge Loss
Section 2.7.1.4.1.3.2.3 - Generalized Smooth Hinge Loss
Section 2.7.1.4.1.3.2.4 - Logistic Loss
Section 2.7.1.4.1.3.2.5 - Cross entropy loss (Log Loss)
Section 2.7.1.4.1.3.2.6 - Sparse and Multi-Hot Sparse Categorical Cross entropy loss (Log Loss)
Section 2.7.1.4.1.3.2.7 - Kullback–Leibler divergence (Relative Entropy)
Section 2.7.1.4.1.3.2.8 - Poisson Loss
Section 2.7.1.4.1.3.2.9 - Cosine Proximity Loss
Section 2.7.1.4.1.3.2.10 - Exponential Loss
Section 2.7.1.4.2 - Reward Functions
Section 2.7.1.4.3 - Profit Functions
Section 2.7.1.4.4 - Utiltity Functions
Section 2.7.1.4.4.0 - Basic Writeup - Wikipedia - Utility Functions
Section 2.7.1.4.4.1 - CES (Constant Elasticity of Substituion) Utility
Section 2.7.1.4.4.2 - Isoelastic Utility
Section 2.7.1.4.4.3 - Exponential Utility
Section 2.7.1.4.4.4 - Quasi-Linear Utility
Section 2.7.1.4.4.5 - Homothetic Preferences
Section 2.7.1.4.4.6 - Stone-Geary Utility
Section 2.7.1.4.4.7 - Von Neumann-Morgenstern Utility
Section 2.7.1.4.4.8 - Hyperbolic Absolute Risk Aversion
Section 2.7.1.4.5 - Demand Functions
Section 2.7.1.4.5.0 - Basic Writeup - Wikipedia - Demand Functions
Section 2.7.1.4.5.1 - Hicksian Demand
Section 2.7.1.4.5.2 - Inverse Demand Function
Section 2.7.1.4.5.3 - Marshallian Demand Function
Section 2.7.1.5 - Optimal control and infinite-dimensional optimization
Section 2.7.1.5.1 - Optimal Control
Section 2.7.1.5.1.0 - Basic Writeup - Wikipedia - Optimal Control
Section 2.7.1.5.1.1 - Pontryagin's minimum principle
Section 2.7.1.5.1.1.0 - Basic Writeup - Wikipedia - Pontryagin's minimum principle
Section 2.7.1.5.1.1.1 - Costate equations
Section 2.7.1.5.1.1.2 - Hamiltonian (control theory)
Section 2.7.1.5.1.2 - Types of problems
Section 2.7.1.5.1.2.1 - Linear-quadratic regulator
Section 2.7.1.5.1.2.2 - Linear-quadratic-Gaussian control (LQG)
Section 2.7.1.5.1.2.2.0 - Basic Writeup - Wikipedia - Linear-quadratic-Gaussian control (LQG)
Section 2.7.1.5.1.2.2.1 - Optimal projection equations
Section 2.7.1.5.1.3 - Algebraic Riccati equation
Section 2.7.1.5.1.4 - Bang–bang control
Section 2.7.1.5.1.5 - Covector mapping principle
Section 2.7.1.5.1.6 - Differential dynamic programming
Section 2.7.1.5.1.7 - DNSS point
Section 2.7.1.5.1.8 - Legendre–Clebsch condition
Section 2.7.1.5.1.9 - Pseudospectral optimal control
Section 2.7.1.5.1.9.0 - Basic Writeup - Wikipedia - Pseudospectral optimal control
Section 2.7.1.5.1.9.1 - Bellman pseudospectral method
Section 2.7.1.5.1.9.2 - Chebyshev pseudospectral method
Section 2.7.1.5.1.9.3 - Flat pseudospectral method
Section 2.7.1.5.1.9.4 - Gauss pseudospectral method
Section 2.7.1.5.1.9.5 - Legendre pseudospectral method
Section 2.7.1.5.1.9.6 - Pseudospectral knotting method
Section 2.7.1.5.1.9.7 - Ross–Fahroo pseudospectral method
Section 2.7.1.5.1.10 - Ross–Fahroo lemma
Section 2.7.1.5.1.11 - Ross' π lemma
Section 2.7.1.5.1.12 - Sethi model
Section 2.7.1.5.2 - Infinite-dimensional optimization
Section 2.7.1.5.2.0 - Basic Writeup - Wikipedia - Infinite-dimensional optimization
Section 2.7.1.5.2.1 - Semi-infinite programming
Section 2.7.1.5.2.2 - Shape and Topology optimization
Section 2.7.1.5.2.2.0 - Basic Writeups
Section 2.7.1.5.2.2.0.1 - Part 1 - Wikipeda - Shape Optimization
Section 2.7.1.5.2.2.0.2 - Part 2 - Wikipeda - Toplogy Optimization
Section 2.7.1.5.2.2.1 - Topological derivative
Section 2.7.1.5.2.3 - Generalized semi-infinite programming
Section 2.7.1.6 - Dealing with Uncertainty and Randomness
Section 2.7.1.6.1 - Approaches to deal with uncertainty
Section 2.7.1.6.1.1 - Markov decision process
Section 2.7.1.6.1.2 - Partially observable Markov decision process
Section 2.7.1.6.1.3 - Robust optimization
Section 2.7.1.6.1.3.0 - Basic Writeup - Wikipedia - Robust optimization
Section 2.7.1.6.1.3.1 - Wald's maximin model
Section 2.7.1.6.1.4 - Scenario optimization
Section 2.7.1.6.1.5 - Stochastic approximation
Section 2.7.1.6.1.6 - Stochastic optimization
Section 2.7.1.6.1.7 - Stochastic programming
Section 2.7.1.6.1.8 - Stochastic gradient descent
Section 2.7.1.6.2 - Random optimization algorithms
Section 2.7.1.6.2.0 - Basic Writeup - Wikipedia - Random optimization algorithms
Section 2.7.1.6.2.1 - Random search
Section 2.7.1.6.2.2 - Simulated annealing
Section 2.7.1.6.2.2.1 - Basic Writeup - Wikipedia - Simulated annealing
Section 2.7.1.6.2.2.2 - Adaptive simulated annealing
Section 2.7.1.6.2.2.3 - Great Deluge algorithm
Section 2.7.1.6.2.2.4 - Mean field annealing
Section 2.7.1.6.2.3 - Bayesian optimization
Section 2.7.1.6.2.4 - Evolutionary algorithm
Section 2.7.1.6.2.4.0 - Basic Writeup - Wikipedia - Evolutionary algorithm
Section 2.7.1.6.2.4.1 - Differential evolution
Section 2.7.1.6.2.4.2 - Evolutionary programming
Section 2.7.1.6.2.4.3 - Genetic algorithm
Section 2.7.1.6.2.4.4 - Genetic programming
Section 2.7.1.6.2.4.5 - Multiple Coordinated Agents Coevolution Evolutionary Algorithm(MCACEA)
Section 2.7.1.6.2.4.6 - Simultaneous perturbation stochastic approximation (SPSA)
Section 2.7.1.6.2.5 - Luus–Jaakola
Section 2.7.1.6.2.6 - Particle swarm optimization
Section 2.7.1.6.2.7 - Stochastic tunneling
Section 2.7.1.6.2.8 - Harmony search
Section 2.7.1.6.2.9 - Monte Carlo method
Section 2.7.1.6.2.9.0 - Basic Writeup - Wikipedia - Monte Carlo method
Section 2.7.1.6.2.9.1 - Variants of the Monte Carlo method
Section 2.7.1.6.2.9.1.1 - Direct simulation Monte Carlo
Section 2.7.1.6.2.9.1.2 - Quasi-Monte Carlo method
Section 2.7.1.6.2.9.1.3 - Markov chain Monte Carlo
Section 2.7.1.6.2.9.1.3.0 - Basic Writeup - Wikipedia - Markov chain Monte Carlo
Section 2.7.1.6.2.9.1.3.1 - Metropolis–Hastings algorithm
Section 2.7.1.6.2.9.1.3.1.0 - Basic Writeup - Wikipedia - Metropolis–Hastings algorithm
Section 2.7.1.6.2.9.1.3.1.1 - Multiple-try Metropolis
Section 2.7.1.6.2.9.1.3.1.2 - Wang and Landau algorithm
Section 2.7.1.6.2.9.1.3.1.3 - Equation of State Calculations by Fast Computing Machines
Section 2.7.1.6.2.9.1.3.1.4 - Multicanonical ensemble
Section 2.7.1.6.2.9.1.3.2 - Gibbs sampling
Section 2.7.1.6.2.9.1.3.3 - Coupling from the past
Section 2.7.1.6.2.9.1.3.4 - Reversible-jump Markov chain Monte Carlo
Section 2.7.1.6.2.9.1.4 - Dynamic Monte Carlo method
Section 2.7.1.6.2.9.1.4.0 - Basic Writeup - Wikipedia - Dynamic Monte Carlo method
Section 2.7.1.6.2.9.1.4.1 - Kinetic Monte Carlo
Section 2.7.1.6.2.9.1.4.2 - Gillespie algorithm
Section 2.7.1.6.2.9.1.5 - Particle filter
Section 2.7.1.6.2.9.1.5.0 - Basic Writeup - Wikipedia - Particle filter
Section 2.7.1.6.2.9.1.5.1 - Auxiliary particle filter
Section 2.7.1.6.2.9.1.6 - Reverse Monte Carlo
Section 2.7.1.6.2.9.1.7 - Demon algorithm
Section 2.7.1.6.2.9.2 - Pseudo-random number sampling
Section 2.7.1.6.2.9.2.0 - Basic Writeup - Wikipedia - Pseudo-random number sampling
Section 2.7.1.6.2.9.2.1 - Inverse transform sampling
Section 2.7.1.6.2.9.2.2 - Rejection sampling
Section 2.7.1.6.2.9.2.2.0 - Basic Writeup - Wikipedia - Rejection Sampling
Section 2.7.1.6.2.9.2.2.1 - Ziggurat algorithm
Section 2.7.1.6.2.9.2.3 - For sampling from a normal distribution
Section 2.7.1.6.2.9.2.3.1 - Box–Muller transform
Section 2.7.1.6.2.9.2.3.2 - Marsaglia polar method
Section 2.7.1.6.2.9.2.4 - Convolution random number generator
Section 2.7.1.6.2.9.2.5 - Indexed search
Section 2.7.1.6.2.9.3 - Variance reduction techniques
Section 2.7.1.6.2.9.3.0 - Basic Writeup - Wikipedia - Variance reduction techniques
Section 2.7.1.6.2.9.3.1 - Antithetic variates
Section 2.7.1.6.2.9.3.2 - Control variates
Section 2.7.1.6.2.9.3.3 - Importance sampling
Section 2.7.1.6.2.9.3.4 - Stratified sampling
Section 2.7.1.6.2.9.3.5 - VEGAS algorithm
Section 2.7.1.6.2.9.4 - Low-discrepancy sequence
Section 2.7.1.6.2.9.4.0 - Basic Writeup - Wikipedia - Low-discrepancy sequence
Section 2.7.1.6.2.9.4.1 - Constructions of low-discrepancy sequences
Section 2.7.1.6.2.9.5 - Event generator
Section 2.7.1.6.2.9.6 - Parallel tempering
Section 2.7.1.6.2.9.7 - Umbrella sampling
Section 2.7.1.6.2.9.8 - Hybrid Monte Carlo
Section 2.7.1.6.2.9.9 - Ensemble Kalman filter
Section 2.7.1.6.2.9.10 - Transition path sampling
Section 2.7.1.6.2.9.11 - Walk-on-spheres method
Section 2.7.1.7 - Theoretical Aspects
Section 2.7.1.7.1 - Convex analysis
Section 2.7.1.7.1.0 - Basic Writeup - Wikipedia - Convex analysis
Section 2.7.1.7.1.1 - Pseudoconvex function
Section 2.7.1.7.1.2 - Quasiconvex function
Section 2.7.1.7.1.3 - Subderivative
Section 2.7.1.7.1.4 - Geodesic convexity
Section 2.7.1.7.2 - Duality (optimization)
Section 2.7.1.7.2.0 - Basic Writeup - Wikipedia - Duality (optimization)
Section 2.7.1.7.2.1 - Perturbation function
Section 2.7.1.7.2.2 - Slater's condition
Section 2.7.1.7.2.3 - Duality gap
Section 2.7.1.7.2.4 - Weak duality
Section 2.7.1.7.2.5 - Strong duality
Section 2.7.1.7.2.6 - Fenchel's duality theorem
Section 2.7.1.7.2.7 - Wolfe duality
Section 2.7.1.7.2.8 - Total dual integrality
Section 2.7.1.7.2.9 - Shadow price
Section 2.7.1.7.2.10 - Dual Cone and Polar Cone
Section 2.7.1.7.3 - Farkas' lemma
Section 2.7.1.7.4 - Karush–Kuhn–Tucker conditions (KKT)
Section 2.7.1.7.4.0 - Basic Writeup - Wikipedia - Karush–Kuhn–Tucker conditions (KKT)
Section 2.7.1.7.4.1 - Fritz John conditions — variant of KKT conditions
Section 2.7.1.7.5 - Lagrange multiplier
Section 2.7.1.7.5.0 - Basic Writeup - Wikipedia - Lagrange multiplier
Section 2.7.1.7.5.1 - Lagrange multipliers on Banach spaces
Section 2.7.1.7.6 - Semi-continuity
Section 2.7.1.7.7 - Complementarity theory
Section 2.7.1.7.7.0 - Basic Writeup - Wikipedia - Complementarity theory
Section 2.7.1.7.7.1 - Mixed complementarity problem
Section 2.7.1.7.7.1.0 - Basic Writeup - Wikipedia - Mixed complementarity problem
Section 2.7.1.7.7.1.1 - Mixed linear complementarity problem
Section 2.7.1.7.7.1.2 - Lemke's algorithm
Section 2.7.1.7.8 - Danskin's theorem
Section 2.7.1.7.9 - Maximum theorem
Section 2.7.1.7.10 - No free lunch in search and optimization
Section 2.7.1.7.11 - Relaxation (approximation)
Section 2.7.1.7.11.0 - Basic Writeup - Wikipedia - Relaxation (approximation)
Section 2.7.1.7.11.1 - Lagrangian relaxation
Section 2.7.1.7.11.2 - Linear programming relaxation
Section 2.7.1.7.12 - Self-concordant function
Section 2.7.1.7.13 - Reduced cost
Section 2.7.1.7.14 - Hardness of approximation
Section 2.7.1.7.15 - Test Functions for Optimization
Section 2.7.1.7.15.0 - Basic Writeup - Wikipedia - Test Functions for Optimization
Section 2.7.1.7.15.1 - Rosenbrock function
Section 2.7.1.7.15.2 - Himmelblau's function
Section 2.7.1.7.15.3 - Rastrigin function
Section 2.7.1.7.15.4 - Shekel function
Section 2.7.2 - Interpolation and Approximation
Section 2.7.2.1 - Interpolation
Section 2.7.2.1.0 - Basic Writeup - Wikipedia - Interpolation
Section 2.7.2.1.1 - Nearest-neighbor interpolation
Section 2.7.2.2 - Polynomial interpolation
Section 2.7.2.2.0 - Basic Writeup - Wikipedia - Polynomial interpolation
Section 2.7.2.2.1 - Linear interpolation
Section 2.7.2.2.2 - Runge's phenomenon
Section 2.7.2.2.3 - Vandermonde matrix
Section 2.7.2.2.4 - Chebyshev polynomials
Section 2.7.2.2.5 - Chebyshev nodes
Section 2.7.2.2.6 - Lebesgue constant (interpolation)
Section 2.7.2.2.7 - Different forms for the interpolant
Section 2.7.2.2.7.1 - Newton polynomial
Section 2.7.2.2.7.1.0 - Basic Writeup - Wikipedia - Newton polynomial
Section 2.7.2.2.7.1.1 - Divided differences
Section 2.7.2.2.7.1.2 - Neville's algorithm
Section 2.7.2.2.7.2 - Lagrange polynomial
Section 2.7.2.2.7.3 - Bernstein polynomial
Section 2.7.2.2.7.4 - Brahmagupta's interpolation formula
Section 2.7.2.2.8 - Extensions to multiple dimensions
Section 2.7.2.2.8.1 - Bilinear interpolation
Section 2.7.2.2.8.2 - Trilinear interpolation
Section 2.7.2.2.8.3 - Bicubic interpolation
Section 2.7.2.2.8.4 - Tricubic interpolation
Section 2.7.2.2.8.5 - Padua points
Section 2.7.2.2.9 - Hermite interpolation
Section 2.7.2.2.11 - Abel–Goncharov interpolation
Section 2.7.2.3 - Spline interpolation
Section 2.7.2.3.0 - Basic Writeups
Section 2.7.2.3.0.1 - Part 1 - Wikipedia - Spline (mathematics)
Section 2.7.2.3.0.2 - Part 2 - Wikipedia - Spline interpolation
Section 2.7.2.3.1 - Perfect spline
Section 2.7.2.3.2 - Cubic Hermite spline
Section 2.7.2.3.2.0 - Basic Writeup - Wikipedia - Cubic Hermite spline
Section 2.7.2.3.2.1 - Centripetal Catmull–Rom spline
Section 2.7.2.3.3 - Monotone cubic interpolation
Section 2.7.2.3.4 - Hermite spline
Section 2.7.2.3.5 - Bézier curve
Section 2.7.2.3.5.0 - Basic Writeup - Wikipedia - Bézier curve
Section 2.7.2.3.5.1 - De Casteljau's algorithm
Section 2.7.2.3.5.2 - Composite Bézier curve
Section 2.7.2.3.5.3 - Generalizations to more dimensions
Section 2.7.2.3.5.3.1 - Bézier triangle
Section 2.7.2.3.5.3.2 - Bézier surface
Section 2.7.2.3.6 - B-spline
Section 2.7.2.3.6.0 - Basic Writeup - Wikipedia - B-spline
Section 2.7.2.3.6.1 - Box spline
Section 2.7.2.3.6.2 - Truncated power function
Section 2.7.2.3.6.3 - De Boor's algorithm
Section 2.7.2.3.7 - Non-uniform rational B-spline (NURBS)
Section 2.7.2.3.7.0 - Basic Writeup - Wikipedia - Non-uniform rational B-spline (NURBS)
Section 2.7.2.3.7.1 - T-spline
Section 2.7.2.3.8 - Kochanek–Bartels spline
Section 2.7.2.3.9 - Coons patch
Section 2.7.2.3.10 - M-spline
Section 2.7.2.3.11 - I-spline
Section 2.7.2.3.12 - Smoothing spline
Section 2.7.2.3.13 - Blossom (functional)
Section 2.7.2.4 - Trigonometric interpolation
Section 2.7.2.4.0 - Basic Writeup - Wikipedia - Trigonometric interpolation
Section 2.7.2.4.1 - Discrete Fourier transform
Section 2.7.2.4.1.0 - Basic Writeup - Wikipedia - Discrete Fourier transform
Section 2.7.2.4.1.1 - Relations between Fourier transforms and Fourier series
Section 2.7.2.4.2 - Fast Fourier transform (FFT)
Section 2.7.2.4.2.0 - Basic Writeup - Wikipedia - Fast Fourier transform (FFT)
Section 2.7.2.4.2.1 - Bluestein's FFT algorithm
Section 2.7.2.4.2.2 - Bruun's FFT algorithm
Section 2.7.2.4.2.3 - Cooley–Tukey FFT algorithm
Section 2.7.2.4.2.4 - Split-radix FFT algorithm
Section 2.7.2.4.2.5 - Goertzel algorithm
Section 2.7.2.4.2.6 - Prime-factor FFT algorithm
Section 2.7.2.4.2.7 - Rader's FFT algorithm
Section 2.7.2.4.2.8 - Bit-reversal permutation
Section 2.7.2.4.2.9 - Butterfly diagram
Section 2.7.2.4.2.10 - Twiddle factor
Section 2.7.2.4.2.11 - Cyclotomic fast Fourier transform
Section 2.7.2.4.2.12 - Methods for computing discrete convolutions with finite impulse response filters using the FFT
Section 2.7.2.4.2.12.1 - Overlap–add method
Section 2.7.2.4.2.12.2 - Overlap–save method
Section 2.7.2.4.3 - Sigma approximation
Section 2.7.2.4.4 - Dirichlet kernel
Section 2.7.2.4.5 - Gibbs phenomenon
Section 2.7.2.5 - Other interpolants
Section 2.7.2.5.1 - Simple rational approximation
Section 2.7.2.5.1.0 - Basic Writeup - Wikipedia - Simple rational approximation
Section 2.7.2.5.1.1 - Polynomial and rational function modeling
Section 2.7.2.5.2 - Wavelet
Section 2.7.2.5.2.0 - Basic Writeup - Wikipedia - Wavelet
Section 2.7.2.5.2.1 - Continuous wavelet
Section 2.7.2.5.2.2 - Transfer matrix
Section 2.7.2.5.2.3 - Discrete wavelet transform (DWT)
Section 2.7.2.5.2.4 - Multiresolution analysis (MRA)
Section 2.7.2.5.2.5 - Lifting scheme
Section 2.7.2.5.2.6 - Binomial QMF (BQMF)
Section 2.7.2.5.2.7 - Fast wavelet transform (FWT)
Section 2.7.2.5.2.8 - Complex wavelet transform
Section 2.7.2.5.2.9 - Complex wavelet transform
Section 2.7.2.5.2.10 - Non or undecimated wavelet transform
Section 2.7.2.5.2.11 - Non or undecimated wavelet transform
Section 2.7.2.5.2.12 - Newland transform
Section 2.7.2.5.2.13 - Wavelet packet decomposition (WPD)
Section 2.7.2.5.2.14 - Stationary wavelet transform (SWT)
Section 2.7.2.5.2.15 - Second generation wavelet transform (SGWT)
Section 2.7.2.5.2.16 - Dual-tree complex wavelet transform (DTCWT)
Section 2.7.2.5.3 - Inverse distance weighting
Section 2.7.2.5.4 - Radial basis function (RBF)
Section 2.7.2.5.4.0 - Basic Writeup - Wikipedia - Radial basis function (RBF)
Section 2.7.2.5.4.1 - Polyharmonic spline
Section 2.7.2.5.4.2 - Thin plate spline
Section 2.7.2.5.4.3 - Hierarchical RBF
Section 2.7.2.5.5 - Subdivision surface
Section 2.7.2.5.5.0 - Basic Writeup - Wikipedia - Subdivision surface
Section 2.7.2.5.5.1 - Catmull–Clark subdivision surface
Section 2.7.2.5.5.2 - Doo–Sabin subdivision surface
Section 2.7.2.5.5.3 - Loop subdivision surface
Section 2.7.2.5.6 - Slerp
Section 2.7.2.5.7 - Irrational base discrete weighted transform
Section 2.7.2.5.8 - Nevanlinna–Pick interpolation
Section 2.7.2.5.8.0 - Basic Writeup - Wikipedia - Nevanlinna–Pick interpolation
Section 2.7.2.5.8.1 - Pick matrix
Section 2.7.2.5.9 - Multivariate interpolation
Section 2.7.2.5.9.0 - Basic Writeup - Wikipedia - Multivariate interpolation
Section 2.7.2.5.9.1 - Barnes interpolation
Section 2.7.2.5.9.2 - Coons surface
Section 2.7.2.5.9.3 - Lanczos resampling
Section 2.7.2.5.9.4 - Natural neighbor interpolation
Section 2.7.2.5.9.5 - Nearest neighbor value interpolation
Section 2.7.2.5.9.6 - PDE surface
Section 2.7.2.5.9.7 - Transfinite interpolation
Section 2.7.2.5.9.8 - Trend surface analysis
Section 2.7.2.5.9.9 - Polynomial interpolation
Section 2.7.2.6 - Approximation theory
Section 2.7.2.6.0 - Basic Writeup - Wikipedia - Approximation theory
Section 2.7.2.6.1 - Orders of approximation
Section 2.7.2.6.2 - Lebesgue's lemma
Section 2.7.2.6.3 - Curve fitting
Section 2.7.2.6.3.0 - Basic Writeup - Wikipedia - Curve fitting
Section 2.7.2.6.3.1 - Vector field reconstruction
Section 2.7.2.6.4 - Modulus of continuity
Section 2.7.2.6.5 - Least squares (function approximation)
Section 2.7.2.6.6 - Minimax approximation algorithm
Section 2.7.2.6.6.0 - Basic Writeup Minimax approximation algorithm
Section 2.7.2.6.6.1 - Equioscillation theorem
Section 2.7.2.6.7 - Unisolvent point set
Section 2.7.2.6.8 - Approximation by polynomials
Section 2.7.2.6.8.1 - Linear approximation
Section 2.7.2.6.8.2 - Bernstein polynomial
Section 2.7.2.6.8.3 - Bernstein's constant
Section 2.7.2.6.8.4 - Remez algorithm
Section 2.7.2.6.8.5 - Bernstein's inequality (mathematical analysis)
Section 2.7.2.6.8.6 - Mergelyan's theorem
Section 2.7.2.6.8.7 - Müntz–Szász theorem
Section 2.7.2.6.8.8 - Bramble–Hilbert lemma
Section 2.7.2.6.8.9 - Discrete Chebyshev polynomials
Section 2.7.2.6.8.10 - Favard's theorem
Section 2.7.2.6.9 - Approximation by Fourier series / trigonometric polynomials
Section 2.7.2.6.9.1 - Jackson's inequality
Section 2.7.2.6.9.1.0 - Basic Writeup - Wikipedia - Jackson's inequality
Section 2.7.2.6.9.1.1 - Bernstein's theorem (approximation theory)
Section 2.7.2.6.9.2 - Fejér's theorem
Section 2.7.2.6.9.3 - Erdős–Turán inequality
Section 2.7.2.6.10 - Different approximations
Section 2.7.2.6.10.1 - Moving least squares
Section 2.7.2.6.10.2 - Padé approximant
Section 2.7.2.6.10.2.0 - Basic Writeup - Wikipedia - Padé approximant
Section 2.7.2.6.10.2.1 - Padé table
Section 2.7.2.6.10.3 - Hartogs–Rosenthal theorem
Section 2.7.2.6.10.4 - Szász–Mirakyan operator
Section 2.7.2.6.10.5 - Szász–Mirakjan–Kantorovich operator
Section 2.7.2.6.10.6 - Baskakov operator
Section 2.7.2.6.10.7 - Favard operator
Section 2.7.2.6.11 - Surrogate model
Section 2.7.2.6.12 - Constructive function theory
Section 2.7.2.6.13 - Universal differential equation
Section 2.7.2.6.14 - Fekete problem
Section 2.7.2.6.15 - Carleman's condition
Section 2.7.2.6.16 - Krein's condition
Section 2.7.2.6.17 - Lethargy theorem
Section 2.7.2.6.18 - Wirtinger's representation and projection theorem
Section 2.7.2.7 - Miscellaneous
Section 2.7.2.7.1 - Extrapolation
Section 2.7.2.7.1.0 - Basic Writeup - Wikipedia - Extrapolation
Section 2.7.2.7.1.1 - Linear predictive analysis
Section 2.7.2.7.2 - Unisolvent functions
Section 2.7.2.7.3 - Regression analysis
Section 2.7.2.7.3.0 - Basic Writeup - Wikipedia - Regression analysis
Section 2.7.2.7.3.1 - Isotonic regression
Section 2.7.2.7.4 - Curve-fitting compaction
Section 2.7.3 - Error Analysis
Section 2.7.3.0 - Basic Writeup - Wikipedia - Error Analysis
Section 2.7.3.1 - Approximation
Section 2.7.3.2 - Types of Errors
Section 2.7.3.2.1 - Approximation Error
Section 2.7.3.2.2 - Discretization error
Section 2.7.3.2.3 - Numerical error
Section 2.7.3.2.4 - Round-off error
Section 2.7.3.2.5 - Truncation error
Section 2.7.3.2.6 - False Precision
Section 2.7.3.3 - Condition number
Section 2.7.3.4 - Loss of significance
Section 2.7.3.5 - Numerical stability
Section 2.7.3.6 - Affine Arithmetic
Section 2.7.3.7 - Relative change and difference
Section 2.7.3.8 - Error propagation
Section 2.7.3.8.1 - Propagation of uncertainty
Section 2.7.3.8.2 - Significance arithmetic
Section 2.7.3.8.3 - Residual (numerical analysis)
