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