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数值分析（英文版）

数值分析（英文版）

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作者: R.Kress 编

出版社: 世界图书出版公司

出版时间: 2003-06

版次: 1

ISBN: 9787506259668

定价: 38.00

装帧: 平装

开本: 其他

纸张: 胶版纸

页数: 326页

分类: 自然科学

13人买过

No applied mathematician can be properly trained without some basic understanding of numerical methods, i.e., numerical analysis. And no scientist and engineer should be using a package program for numerical computations without understanding the program's purpose and its limitations. This book is an attempt to provide some of the required knowledge and understanding. It is written in a spirit that considers numerical analysis not merely as a tool fer solving applied problems but also as a challenging and rewarding part of mathematics. The main goal is to provide insight into numerical analysis rather than merely to provide numerical recipes. 1 Introduction

2 Linear Systems

  2.1 Examples for Systems of Equations

  2.2 Gaussian Elimination

  2.3 LR Decomposition

  2.4 QR Decomposition

  Problems

3 Basic Functional Analysis

  3.1 Normed Spaces

  3.2 Scalar Products

  3.3 Bounded Linear Operators

  3.4 Matrix Norms

  3.5 Completeness

  3.6 The Banach Fixed Point Theorem

  3.7 Best Approximation

  Problems

4 Iterative Methods for Linear Systems

  4.1 Jacobi and Gauss-Seidel Iterations

  4.2 Relaxation Methods

  4.3 Two-Grid Methods

  Problems

5 III-Conditioned Linear Systems

6 Iterative Methods for Nonlinear Systems

7 Matrix Eigenvalue Problems

8 Interpolation

9 Numerical Integration

10 Initial Value Problems

11 Boundary Value Problems

12 Integral Equations

References

Index
内容简介:
No applied mathematician can be properly trained without some basic understanding of numerical methods, i.e., numerical analysis. And no scientist and engineer should be using a package program for numerical computations without understanding the program's purpose and its limitations. This book is an attempt to provide some of the required knowledge and understanding. It is written in a spirit that considers numerical analysis not merely as a tool fer solving applied problems but also as a challenging and rewarding part of mathematics. The main goal is to provide insight into numerical analysis rather than merely to provide numerical recipes.
目录:
1 Introduction

2 Linear Systems

  2.1 Examples for Systems of Equations

  2.2 Gaussian Elimination

  2.3 LR Decomposition

  2.4 QR Decomposition

  Problems

3 Basic Functional Analysis

  3.1 Normed Spaces

  3.2 Scalar Products

  3.3 Bounded Linear Operators

  3.4 Matrix Norms

  3.5 Completeness

  3.6 The Banach Fixed Point Theorem

  3.7 Best Approximation

  Problems

4 Iterative Methods for Linear Systems

  4.1 Jacobi and Gauss-Seidel Iterations

  4.2 Relaxation Methods

  4.3 Two-Grid Methods

  Problems

5 III-Conditioned Linear Systems

6 Iterative Methods for Nonlinear Systems

7 Matrix Eigenvalue Problems

8 Interpolation

9 Numerical Integration

10 Initial Value Problems

11 Boundary Value Problems

12 Integral Equations

References

Index

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