矩陣計算（英文版·第3版）

內容簡介

本書是數值計算領域的名著，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、矩陣函式及專題討論等。書中的許多算法都有現成的軟體包實現，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。

1Matrix Multiplication Problems1

1.1Basic Algorithms and Notation2

1.2Exploiting Structure 16

1.3Block Matrices and Algorithms24

1.4Vectorization and Re-Use Issues34

2Matrix Analysis48

2.1Basic Ideas from Linear Algebra48

2.2Vector Norms 52

2.3Matrix Norms 54

2.4Finite Precision Matrix Computations59

2.5Orthogonality and the SVD69

2.6Projections and the CS Decomposition75

2.7The Sensitivity of Square Linear Systems80

3General Linear Systems87

3.1Triangular Systems88

3.2The LU Factorization94

3.3Roundoff Analysis of Gaussian Elimination104

3.4Pivoting109

3.5Improving and Estimating Accuracy123

4Special Linear Systems

4.1The LDMT and LDLT Factorizations135

4.2Positive Definite Systems140

4.3Banded Systems152

4.4Symmetric Indefinite Systems161

4.5Block Systems174

4.6Vandermonde Systems and the FFT183

4.7Toeplitz and Related Systems193