Numerical Analysis Notes and Codes. XeLaTeX to compile. (option: '-shell-escape')
- 1.1: Review of Calculus
- 1.2: Round-off Errors and Computer Arithmetic
- 1.3: Algorithms and Convergence
- 1.4: Numerical Software
- 2.1 The Bisection Method
- 2.2 Fixed-Point Iteration
- 2.3 Newton's Method and Its Extensions
- 2.4 Error Analysis for Iterative Methods
- 2.5 Accelerating Convergence
- 2.6 Zeros of Polynomials and Müller's Method
- 2.7 Survey of Methods and Software
- 3.1 Interpolation and the Lagrange Polynomial
- 3.2 Data Approximation and Neville's Method
- 3.3 Divided Differences
- 3.4 Hermite Interpolation
- 3.5 Cubic Spline Interpolation
- 3.6 Parametric Curves
- 3.7 Survey of Methods and Software
- 4.1 Numerical Differentiation
- 4.2 Richardson's Extrapolation
- 4.3 Elements of Numerical Integration
- 4.4 Composite Numerical Integration
- 4.5 Romberg Integration
- 4.6 Adaptive Quadrature Methods
- 4.7 Gaussian Quadrature
- 4.8 Multiple Integrals
- 4.9 Improper Integrals
- 4.10 Survey of Methods and Software
- 5.1 The Elementary Theory of Initial-Value Problems
- 5.2 Euler’s Method
- 5.3 Higher-Order Taylor Methods
- 5.4 Runge-Kutta Methods
- 5.5 Error Control and the Runge-Kutta-Fehlberg Method
- 5.6 Multistep Methods
- 5.7 Variable Step-Size Multistep Methods
- 5.8 Extrapolation Methods
- 5.9 Higher-Order Equations and Systems of Differential Equations
- 5.10 Stability
- 5.11 Stiff Differential Equations
- 5.12 Survey of Methods and Software
- 6.1 Linear Systems of Equations
- 6.2 Pivoting Strategies
- 6.3 Linear Algebra and Matrix Inversion
- 6.4 The Determinant of a Matrix
- 6.5 Matrix Factorization
- 6.6 Special Types of Matrices
- 6.7 Survey of Methods and Software
- 7.1 Norms of Vectors and Matrices
- 7.2 Eigenvalues and Eigenvectors
- 7.3 The Jacobi and Gauss-Siedel Iterative Techniques
- 7.4 Relaxation Techniques for Solving Linear Systems
- 7.5 Error Bounds and Iterative Refinement
- 7.6 The Conjugate Gradient Method
- 7.7 Survey of Methods and Software
- 8.1 Discrete Least Squares Approximation
- 8.2 Orthogonal Polynomials and Least Squares Approximation
- 8.3 Chebyshev Polynomials and Economization of Power Series
- 8.4 Rational Function Approximation
- 8.5 Trigonometric Polynomial Approximation
- 8.6 Fast Fourier Transforms
- 8.7 Survey of Methods and Software
- 9.1 Linear Algebra and Eigenvalues
- 9.2 Orthogonal Matrices and Similarity Transformations
- 9.3 The Power Method
- 9.4 Householder’s Method
- 9.5 The QR Algorithm
- 9.6 Singular Value Decomposition
- 9.7 Survey of Methods and Software
- 10.1 Fixed Points for Functions of Several Variables
- 10.2 Newton’s Method
- 10.3 Quasi-Newton Methods
- 10.4 Steepest Descent Techniques
- 10.5 Homotopy and Continuation Methods
- 10.6 Survey of Methods and Software
- 11.1 The Linear Shooting Method
- 11.2 The Shooting Method for Nonlinear Problems
- 11.3 Finite-Difference Methods for Linear Problems
- 11.4 Finite-Difference Methods for Nonlinear Problems
- 11.5 The Rayleigh-Ritz Method
- 11.6 Survey of Methods and Software