矩阵计算
| 矩阵计算 |
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矩阵计算,是一本专业用书。本书系统介绍了矩阵计算的基本理论和方法。内容包括矩阵乘法、矩阵分析、线性方程组、正交化和最小二乘法、特征值问题、Lanczos方法、矩阵函数及专题讨论等。书中的许多算法都有现成的软件包实现，每节后还附有习题，并有注释和大量参考文献。
本书可作为高等学校数学系高年级本科生和研究生的教材，亦可作为计算数学和工程技术人员的参考用书。
目录
简介
Gene H.Golub，（1932-2007），美国科学院、工程院和艺术科学院院士，世界著名的数分析专家，现代矩阵计算的奠基人，生前曾任斯坦福大学教授。他是矩阵分解算法的主要贡献者，与William Kahan在1970年给出了奇异值分解（SingularValue Decomposition,SVD）的可行算法，一直沿用至今。他发起组织了工业与应用数学国际会议（Intemational Congress on Industrial and Applied Mathematics，ICIAM）。
评价
1Matrix Multiplication Problems
1.1Basic Algorithms and Notation
1.2Exploiting Structure
1.3Block Matrices and Algorithms
1.4Vectorization and Re-Use Issues
2Matrix Analysis
2.1Basic Ideas from Linear Algebra
2.2Vector Norms
2.3Matrix Norms
2.4Finite Precision Matrix Computations
2.5Orthogonality and the SVD
2.6Projections and the CS Decomposition
2.7The Sensitivity of Square Linear Systems
3General Linear Systems
3.1Triangular Systems
3.2The LU Factorization
3.3Roundoff Analysis of Gaussian Elimination
3.4Pivoting
3.5Improving and Estimating Accuracy
4Special Linear Systems
4.1The LDMT and LDLT Factorizations
4.2Positive Definite Systems
4.3Banded Systems
4.4Symmetric Indefinite Systems
4.5Block Systems
4.6Vandermonde Systems and the FFT
4.7Toeplitz and Related Systems
5Orthogonalization and Least Squares
5.1Householder and Givens Matrices
5.2The QR Factorization
5.3The Full Rank LS Problem
5.4Other Orthogonal Factorizations
5.5The Rank Deficient LS Problem
5.6Weighting and Iterative Improvement
5.7Square and Underdetermined Systems
6Parallel Matrix Computations
6.1Basic Concepts
6.2Matrix Multiplication
6.3Factorizations
7The Unsymmetric Eigenvalue Problem
8The Symmetric Eigenvalue Problem
9Lanczos Methods
10Iterative Methods for Linear Systems
11Functions of Matrices
12Special Topics
Index[1]