矩陣計算
| 矩陣計算 |
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矩陣計算,是一本專業用書。本書系統介紹了矩陣計算的基本理論和方法。內容包括矩陣乘法、矩陣分析、線性方程組、正交化和最小二乘法、特徵值問題、Lanczos方法、矩陣函數及專題討論等。書中的許多算法都有現成的軟件包實現，每節後還附有習題，並有注釋和大量參考文獻。
本書可作為高等學校數學系高年級本科生和研究生的教材，亦可作為計算數學和工程技術人員的參考用書。
目錄
簡介
Gene H.Golub，（1932-2007），美國科學院、工程院和藝術科學院院士，世界著名的數分析專家，現代矩陣計算的奠基人，生前曾任斯坦福大學教授。他是矩陣分解算法的主要貢獻者，與William Kahan在1970年給出了奇異值分解（SingularValue Decomposition,SVD）的可行算法，一直沿用至今。他發起組織了工業與應用數學國際會議（Intemational Congress on Industrial and Applied Mathematics，ICIAM）。
評價
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]