导语

  

内容提要

  

    葛志昊，徐琛梅编著的《计算方法（英文版）》为普通高校类数学专业教材，全书用英文编写，符合《数值分析》大纲要求，适用于理科数学类专业本科生及其他理工科硕士研究生”数值分析”课程，旨在提高学生的专业英语能力，更适应当前对国际化的要求。
    该教材共8章内容，包括引言（数值计算方法及其内容介绍、误差理论）、插值、最佳逼近理论、数值积分与数值微分、求解线性代数方程组、矩阵特征值近似求解、非线性方程数值解法、常微分方程组的数值解法，并且每章配有习题。

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