计算方法

Chapter 1 Introduction
1．1 Numerical Computational Methods and Main Contents
1．2 Error
1．3 Stability Analysis of Numerical Methods
1．4 How to Avoid Error
Excises 1

Chapter 2 Interpolation and Polynomial Approximation
2．1 Introduction
2．2 Lagrange Interpolation Polynomial
2．3 Neville' s Interpolating Formula
2．4 Newton Interpolation
2．5 Hermite Interpolation
2．6 Piecewise Polynomial Approximation
2．7 Cubic Spline Interpolation
Excises 2

Chapter 3 Approximation Theory
3．1 Optimal Approximation
3．2 Optimal Approximation of Normed Linear Space
3．3 Optimal Uniform Approximation Polynomial
3．4 Minimum Error to Zero-Chebyshev Polynomial
3．5 Optimal Approximation of the Inner Product Space
3．6 Optimal Square Approximation and Orthogonal Polynomials
3．7 Discrete Optimal Square Approximation and Least Square Method （L-S）
Excises 3

Chapter 4 Numerical Integration and Differentiation
4．1 Introduction
4．2 Newton-Cotes Quadrature Formula
4．3 Composite Numerical Integration
4．4 Richardson Extrapolation and Romberg Integration
4．5 Gaussian Quadrature
4．6 Numerical Differentiation
Excises 4

Chapter 5 Solving Linear System of Equations
5．1 Elementary Notions and Results of Linear Algebra
5．2 Direct Methods for Solving Linear System of Equations
5．3 Error of Gaussian Elimination
5．4 Iterative Methods for Solving Linear Systems
5．5 Conjugate Gradient Method
Excises 5

Chapter 6 Approximating Eigenvalues
6．1 Linear Algebra and Eigenvalues
6．2 The Power Method and the Inverse Power Method
6．3 Householder' s Method
6．4 QR Algorithm
6．5 Improved Power Method
Excises 6

Chapter 7 Numerical Solutions of Nonlinear Systems
7．1 The Bisection Method
7．2 Fixed Point Iterative Method
7．3 Newton' s Iteration Method
7．4 Numerical Solutive for Nonlinear Systems of Equations
Excises 7

Chapter 8 Numerical Solutions of Ordinary Differential Equations
8．1 Introduction
8．2 Euler's Method
8．3 Multistep Methods （Ⅰ）
8．4 Muhistep Methods （Ⅱ）
8．5 Runge-Kutta Method
8．6 Stiff Problem
8．7 Numerical Solution for Boundary-value Problem
Excises 8
References