數(shù)值分析

內(nèi)容概要

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.

書籍目錄

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   Problems5 III-Conditioned Linear Systems6 Iterative Methods for Nonlinear Systems7 Matrix Eigenvalue Problems8 Interpolation9 Numerical Integration10 Initial Value Problems11 Boundary Value Problems12 Integral EquationsReferencesIndex

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