Code for Numerical Analysis.
- 0.1 Evaluating a Polynomial
- 0.2 Binary Numbers
- 0.3 Floating Point Representation of Real Numbers
- 0.4 Loss of Significance
- 0.5 Review of Calculus
- 1.1 The Bisection Method
- 1.2 Fixed-Point Iteration
- 1.3 Limits of Accuracy
- 1.4 Newton’s Method
- 1.5 Root-Finding without Derivatives
- 2.1 Gaussian Elimination
- 2.2 The LU Factorization
- 2.3 Sources of Error
- 2.4 The
$PA = LU$ Factorization - 2.5 Iterative Methods
- 2.6 Methods for symmetric positive-definite matrices
- 2.7 Nonlinear Systems of Equations
- 3.1 Data and Interpolating Functions
- 3.2 Interpolation Error
- 3.3 Chebyshev Interpolation
- 3.4 Cubic Splines
- 3.5 Bézier Curves
- 4.1 Least Squares and the Normal Equations
- 4.2 A Survey of Models
- 4.3 QR Factorization
- 4.4 Generalized Minimum Residual (GMRES) Method
- 4.5 Nonlinear Least Squares
- 5.1 Numerical Differentiation
- 5.2 Newton–Cotes Formulas for Numerical Integration
- 5.3 Romberg Integration
- 5.4 Adaptive Quadrature
- 5.5 Gaussian Quadrature
- 6.1 Initial Value Problems
- 6.2 Analysis of IVP Solvers
- 6.3 Systems of Ordinary Differential Equations
- 6.4 Runge–Kutta Methods and Applications
- 6.5 Variable Step-Size Methods
- 6.6 Implicit Methods and Stiff Equations
- 6.7 Multistep Methods
- 7.1 Shooting Method
- 7.2 Finite Difference Methods
- 7.3 Collocation and the Finite Element Method
- 8.1 Parabolic Equations
- 8.2 Hyperbolic Equations
- 8.3 Elliptic Equations
- 8.4 Nonlinear Partial Differential Equations
- 9.1 Random Numbers
- 9.2 Monte Carlo Simulation
- 9.3 Discrete and Continuous Brownian Motion
- 9.4 Stochastic Differential Equations
- 10.1 The Fourier Transform
- 10.2 Trigonometric Interpolation
- 10.3 The FFT and Signal Processing
- 11.1 The Discrete Cosine Transform
- 11.2 Two-Dimensional DCT and Image Compression
- 11.3 Huffman Coding
- 11.4 Modified DCT and Audio Compression
- 12.1 Power Iteration Methods
- 12.2 QR Algorithm
- 12.3 Singular Value Decomposition
- 12.4 Applications of the SVD
- 13.1 Unconstrained Optimization without Derivatives
- 13.2 Unconstrained Optimization with Derivatives