Nonlinear Equations and Optimization
Numerical Methods for Data Science
Preface
1
Introduction
Background Plus a Bit
2
Julia programming
3
Performance Basics
4
Linear Algebra
5
Calculus and analysis
6
Optimization theory
7
Probability
Fundamentals in 1D
8
Notions of Error
9
Floating Point
10
Approximation
11
Automatic Differentiation
12
Numerical Differentiation
13
Quadrature
14
Root Finding and Optimization
15
Computing with Randomness
Numerical Linear Algebra
16
Linear Systems
17
Least Squares
18
Eigenvalue Problems and the SVD
19
Signals and Transforms
20
Stationary Iterations
21
Krylov Subspaces
Nonlinear Equations and Optimization
22
Calculus Revisited
23
Nonlinear Equations and Unconstrained Optimization
24
Continuation and Bifurcation
25
Constrained Optimization
26
Nonlinear Least Squares
Computing with Randomness
27
Sampling
28
Quadrature and Monte Carlo
29
Solvers from Monte Carlo to Las Vegas
30
Uncertainty Quantification
Dimension Reduction and Latent Factor Models
31
Latent Factors and Matrix Factorization
32
From Matrices to Tensors
33
Nonlinear Dimensionality Reduction
Function Approximation
34
Fundamental Concepts
35
Low-Dimensional Structure
36
Kernels and RBFs
37
Neural Networks
Network Analysis
38
Graphs and Matrices
39
Functions on Graphs
40
Clustering and Partitioning
41
Centrality Measures
Learning Dynamics
42
Fundamentals
43
Model Reduction
44
Learning Linear Dynamics
45
Extrapolation and Acceleration
46
From Markov to Koopman
47
Learning Nonlinear Dynamics
References
Nonlinear Equations and Optimization
21
Krylov Subspaces
22
Calculus Revisited