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数值分析【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

袁东锦编著著
出版社：南京：东南大学出版社
ISBN：7810898744
出版时间：2005
标注页数：269页
文件大小：7MB
文件页数：278页
主题词：数值计算－高等学校－教材－英文

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图书目录

1 Preliminaries1

1.1 Review of Calculus1

Exercise7

1.2 Round-Off Errors and Computer Arithmetic7

Exercise17

2 The Solution of Nonlinear Equation f(x)=019

2.1 The Bisection Algorithm20

Exercise25

2.2 Fixed-Point Iteration25

Exercise33

2.3 The Newton-Raphson Method34

Exercise42

2.4 Error Analysis for Iterative Methods and Acceleration Techniques42

Exercise51

3 Interpolation and Polynomial Approximation52

3.1 Interpolation and the Lagrange Polynomial53

Exercise61

3.2 Divided Differences62

Exercise70

3.3 Hermite Interpolation72

Exercise78

3.4 Cubic Spline Interpolation79

4 Numerical Integration88

4.1 Introduction to Quadrature89

Exercise97

4.2 Composite Trapezoidal and Simpson's Rule98

Exercise108

4.3 Recursive Rules and Romberg Integration109

Exercise120

5 Direct Methods for Solving Linear Systems122

5.1 Linear Systems of Equations122

Exercise130

5.2 Pivoting Strategies130

Exercise137

5.3 Matrix Factorization137

Exercise145

5.4 Special Types of Matrices145

Exercise157

6 Iterative Techniques in Matrix Algebra158

6.1 Norms of Vectors and Matrices158

Exercise166

6.2 Eigenvalues and Eigenvectors167

Exercise171

6.3 Iterative Techniques for Solving Linear Systems172

Exercise184

6.4 Error Estimates and Iterative Refinement185

Exercise193

7 Approximating Eigenvalues194

7.1 Linear Algebra and Eigenvalues194

Exercise200

7.2 The Power Method201

Exercise214

7.3 Householder's Method215

Exercise222

7.4 The QR Algorithm223

Exercise233

8 Initial-Value Problems for Ordinary Differential Equations235

8.1 The Elementary Theory of Initial-Value Problems235

Exercise240

8.2 Euler's Method240

Exercise247

8.3 Higher-Order Taylor Methods248

Exercise252

8.4 Runge-Kutta Methods253

Exercise260

8.5 Error Control and the Runge-Kutta-Fehlberg Method261

Exercise267

References269