《矩陣計(jì)算(英文版?第4版)》是數(shù)值計(jì)算領(lǐng)域的名著，系統(tǒng)介紹了矩陣計(jì)算的基本理論和方法。內(nèi)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、特征值問題、Lanczos方法、矩陣函數(shù)及專題討論等。書中的許多算法都有現(xiàn)成的軟件包實(shí)現(xiàn)，每節(jié)后附有習(xí)題，并有注釋和大量參考文獻(xiàn)。新版增加約四分之一內(nèi)容，反映了近年來矩陣計(jì)算領(lǐng)域的飛速發(fā)展。
《矩陣計(jì)算(英文版?第4版)》可作為高等院校數(shù)學(xué)系高年級本科生和研究生教材，亦可作為計(jì)算數(shù)學(xué)和工程技術(shù)人員參考書。
現(xiàn)代矩陣計(jì)算奠基人Gene H. Golub名著，國際上關(guān)于數(shù)值線性代數(shù)方面、的一本專著，被美國加州大學(xué)、斯坦福大學(xué)、華盛頓大學(xué)、芝加哥大學(xué)、中國科學(xué)院研究生院等眾多世界知名學(xué)府用作相關(guān)課程教材或主要參考書。
書中系統(tǒng)介紹了矩陣計(jì)算的基本理論和方法，提及的許多算法都有現(xiàn)成的軟件包實(shí)現(xiàn)。每節(jié)后附有習(xí)題，并給出了大量注釋和參考文獻(xiàn)，有助于讀者自學(xué)和鞏固正文內(nèi)容。
第4版全新改版，新增了約四分之一內(nèi)容，包括張量計(jì)算、快速變換、并行LU等主題，反映了近年來矩陣計(jì)算領(lǐng)域的進(jìn)展。
Gene H. Golub (1932－2007) 生前曾任美國科學(xué)院、工程院和藝術(shù)科學(xué)院院士，世界著名數(shù)值分析專家，現(xiàn)代矩陣計(jì)算奠基人，矩陣分解算法的主要貢獻(xiàn)者。曾長期擔(dān)任斯坦福大學(xué)教授。
Charles F. Van Loan 著名數(shù)值分析專家，美國康奈爾大學(xué)教授，曾任該校計(jì)算機(jī)科學(xué)系主任。他于1973年在密歇根大學(xué)獲得博士學(xué)位，師從Cleve Moler。
1 Matrix Multiplication
1.1 Basic Algorithms and Notation
1.2 Structure and Efficiency
1.3 Block Matrices and Algorithms
1.4 Fast Matrix-Vector Products
1.5 Vectorization and Locality
1.6 Parallel Matrix Multiplication
2 Matrix Analysis
2.1 Basic Ideas from Linear Algebra
2.2 Vector Norms
2.3 Matrix Norms
2.4 The Singular Value Decomposition
2.5 Subspace Metrics
2.6 The Sensitivity of Square Systems
2.7 Finite Precision Matrix Computations
3 General Linear Systems
3.1 Triangular Systems
3.2 The LU Factorization
3.3 Roundoff Error in Gaussian Elimination
3.4 Pivoting
3.5 Improving and Estimating Accuracy
3.6 Parallel LU
4 Special Linear Systems
4.1 Diagonal Dominance and Symmetry
4.2 Positive Definite Systems
4.3 Banded Systems
4.4 Symmetric Indefinite Systems
4.5 Block Tridiagonal Systems
4.6 Vandermonde Systems
4.7 Classical Methods for Toeplitz Systems
4.8 Circulant and Discrete Poisson Systems
5 Orthogonalization and Least Squares
5.1 Householder and Givens Transformations
5.2 The QR Factorization
5.3 The Full-Rank Least Squares Problem
5.4 Other Orthogonal Factorizations
5.5 The Rank-Deficient Least Squares Problem
5.6 Square and Underdetermined Systems
6 Modified Least Squares Problems and Methods
6.1 Weighting and Regularization
6.2 Constrained Least Squares
6.3 Total Least Squares
6.4 Subspace Computations with the SVD
6.5 Updating Matrix Factorizations
7 Unsymmetric Eigenvalue Problems
7.1 Properties and Decompositions
7.2 Perturbation Theory
7.3 Power Iterations
7.4 The Hessenberg and Real Schur Forms
7.5 The Practical QR Algorithm
7.6 Invariant Subspace Computations
7.7 The Generalized Eigenvalue Problem
7.8 Hamiltonian and Product Eigenvalue Problems
7.9 Pseudospectra
8 Symmetric Eigenvalue Problems
8.1 Properties and Decompositions
8.2 Power Iterations
8.3 The Symmetric QR Algorithm
8.4 More Methods for Tridiagonal Problems
8.5 Jacobi Methods
8.6 Computing the SVD
8.7 Generalized Eigenvalue Problems with Symmetry
9 Functions of Matrices
9.1 Eigenvalue Methods
9.2 Approximation Methods
9.3 The Matrix Exponential
9.4 The Sign, Square Root, and Log of a Matrix
10 Large Sparse Eigenvalue Problems
10.1 The Symmetric Lanczos Process
10.2 Lanczos, Quadrature, and Approximation
10.3 Practical Lanczos Procedures
10.4 Large Sparse SVD Frameworks
10.5 Krylov Methods for Unsymmetric Problems
10.6 Jacobi-Davidson and Related Methods
11 Large Sparse Linear System Problems
11.1 Direct Methods
11.2 The Classical Iterations
11.3 The Conjugate Gradient Method
11.4 Other Krylov Methods
11.5 Preconditioning
11.6 The Multigrid Framework
12 Special Topics
12.1 Linear Systems with Displacement Structure
12.2 Structured-Rank Problems
12.3 Kronecker Product Computations
12.4 Tensor Unfoldings and Contractions
12.5 Tensor Decompositions and Iterations
Index
"多年來，這本書一直是我在研究生院講授`數(shù)值線性代數(shù)`的教材。"
——袁亞湘，中科院院士，中國運(yùn)籌學(xué)學(xué)會理事長，馮康獎得主
"本書內(nèi)容非常豐富，有老而經(jīng)典的，也有新的正在研究中的課題。論你是數(shù)值線性代數(shù)領(lǐng)域的工作人員，還是學(xué)生，這都是一本有價(jià)值的參考書。"
——SIAM Review
"這是一部見解深刻、內(nèi)容豐富的經(jīng)典教材，引人深入思考。……沒有比它更好的矩陣計(jì)算參考書了。"
——美國數(shù)學(xué)及應(yīng)用研究所
