數值分析杜睿 9787576608243 【台灣高等教育出版社】

Name: 數值分析 杜睿 9787576608243 【台灣高等教育出版社】
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物品所在地：中國大陸
原出版社：東南大學

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書名：數值分析
ISBN：9787576608243
出版社：東南大學
著編譯者：杜睿
頁數：268
所在地：中國大陸 *此為代購商品
書號：1563589
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內容簡介

本書包括緒論、非線性方程的解法、線性方程組的數值解法、多項式插值、函數逼近、數值積分和數值微分、常微分方程數值解法和偏微分方程數值解法等8章，主要介紹了數值分析的基本概念、演算法的構造和演算法的理論分析等內容。各章末還配有習題和上機編程實驗題，供讀者練習使用。本書結構完整，條理清晰，內容豐富，既可作為國內開設全英文或雙語數值分析課程的本科生、研究生教材或教學參考用書，也可供從事科學計算的相關人員參考。

1 Introduction
1 1 Error
1 1 1 Sources of Approximation
1 1 2 Absolute Error and Relative Error
1 1 3 Significant Digits (or Figures)
1 1 4 Error Estimation of a Function
1 2 Computer Arithmetic
1 3 Numerical Stability
1 4 Ill-Conditioned Problem
1 5 Hornor's Method
Exercise 1
2 Solutions of Equations in One Variable
2 1 Introduction
2 2 The Bisection Method
2 3 Fixed-Point Iteration
2 3 1 Fixed-Point Iteration
2 3 2 Convergence
2 3 3 Order of Convergence
2 3 4 Aitken Method
2 4 Newton's Method
2 4 1 Local Convergence of Newton's Method
2 4 2 Modified Newton's Method for on Equation with Multiple Roots
2 4 3 The Secant Method
2 5 Zeros of Polynomials
2 5 1 Distribution of Zeros of Real Coefficient Polynomials
2 5 2 Bairstov Method
Exercise 2
3 Numerical Methods for Linear System
3 1 Direct Method
3 1 1 Gaussian Elimination Method
3 1 2 Gaussian Elimination Method with Partial Pivoting
3 1 3 Thomas Algorithm for Tridiagonal System
3 2 Matrix Factorization
3 2 1 Matrix Factorization
3 2 2 Matrix Factorization for the Symmetric Matrix
3 2 3 Matrix Factorization of Gaussian Elimination Method with Partial Pivoting
3 3 Norms and Error Analysis
3 3 1 Norms of Vectors
3 3 2 Norms of Matrices
3 3 3 Error Analysis
3 4 Iterative Methods
3 4 1 Jacobi Iterative Method
3 4 2 Gauss-Seidel Iterative Method
3 4 3 Successive Over-Relaxation Method
3 4 4 Convergency of Iterative Method
3 5 Power Method
Exercise 3
4 Interpolation
4 1 Lagrange Interpolating Polynomials
4 2 Newton's Divided-Difference Formula
4 2 1 Divided Difference
4 2 2 Forward Difference and Newton's Forward-Difference Formula
4 3 Hermite InterpoJation
4 4 PieeewisePolynomial Interpolation
4 4 1 Error Analysis of High-Degree Interpolating Polynomials
4 4 2 Piecewise-Linear Interpolation
4 4 3 Piecewise Hermite Interpolation
4 5 Cubic Spline Interpolation
4 5 1 Cubic Splines
4 5 2 Construction of a Cubic Spline
4 5 3 Converqence of Cubic Spline
Exercise 4
5 Approximation Theory
5 1 Best Uniform Approximation
5 1 1 Normed Linear Space
5 1 2 Polynomial of Best Uniform Approximation
5 2 Least Squares Approximation
5 2 1 Inner Product Space
5 2 2 Least Squares Approximation
5 2 3 Least Squares Approximation to Continuous Function
5 2 4 Least Squares Solution of Overdetermined Linear Equations
5 2 5 Discrete Least Squares Approximation
Exercise 5
6 Numerical Integration and Differentiation
6 1 Elements of Numerical Integration
6 1 1 Newton-Cotes Formula
6 1 2 Measuring Precision
6 1 3 Errors of Trapezoidal Rule Simpson's Rule and Boole's Rule
6 1 4 Stability
6 2 Composite Numerical Integration
6 2 1 Composite Trapezoidal Rule
6 2 2 Composite Simpson's Rule
6 2 3 Composite Boole's Rule
6 3 Romberg Integration
6 4 Gaussian Quadrature
6 4 1 Orthogonal Polynomials
6 4 2 Truncation Error of Gaussian Quadrature
6 4 3 Stability and Convergence
6 5 Numerical Differentiation
Exercise 6
7 Initial-Value Problems for Ordinary Differential Equations
7 1 Euler's Method
7 1 1 Euler's Explicit Method
7 1 2 Euler's Implicit Method
7 1 3 Trapezoidal Method
7 1 4 Modified Euler's Method
7 1 5 Global Truncation Error
7 2 Runge-Kutta Methods
7 2 1 Second-Order Runge-Kutta Method
7 2 2 High-Order Runge-Kutta Method
7 2 3 Implicit Runge-Kutta Method
7 3 Stability and Convergence of One-Step Method
7 4 Multistep Methods
7 4 1 Adams Methods
7 4 2 Taylor Methods
7 4 3 Convergency and Stability of Multistep Methods
Exercise 7
8 Numerical Methods for Partial Differential Equations
8 1
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