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。
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
1 Matrix Multiplication Problems
1.1 Basic Algorithms and Notation
1.2 Exploiting Structure
1.3 Block Matrices and Algorithms
1.4 Vectorization and Re-Use Issues
2 Matrix Analysis
2.1 Basic Ideas from Linear Algebra
2.2 Vector Norms
2.3 Matrix Norms
2.4 Finite Precision Matrix Computations
2.5 Orthogonality and the SVD
2.6 Projections and the CS Decomposition
2.7 The Sensitivity of Square Linear Systems
3 General Linear Systems
3.1 Triangular Systems
3.2 The LU Factorization
3.3 Roundoff Analysis of Gaussian Elimination
3.4 Pivoting
3.5 Improving and Estimating Accuracy
4 Special Linear Systems
4.1 The LDMT and LDLT Factorizations
4.2 Positive Definite Systems
4.3 Banded Systems
4.4 Symmetric Indefinite Systems
4.5 Block Systems
4.6 Vandermonde Systems and the FFT
4.7 Toeplitz and Related Systems
5 Orthogonalization and Least Squares
5.1 Householder and Givens Matrices
5.2 The QR Factorization
5.3 The Full Rank LS Problem
5.4 Other Orthogonal Factorizations
5.5 The Rank Deficient LS Problem
5.6 Weighting and Iterative Improvement
5.7 Square and Underdetermined Systems
6 Parallel Matrix Computations
6.1 Basic Concepts
6.2 Matrix Multiplication
6.3 Factorizations
7 The Unsymmetric Eigenvalue Problem
8 The Symmetric Eigenvalue Problem
9 Lanczos Methods
10 Iterative Methods for Linear Systems
11 Functions of Matrices
12 Special Topics
Index
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