矩阵计算(英文版·第3版)(图灵原版数学·统计学系列)
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品牌: Gene H.Golub
基本信息·出版社：人民邮电出版社
·页码：644 页
·出版日期：2009年
·ISBN：7115208808/9787115208804
·条形码：9787115208804
·包装版本：3版
·装帧：平装
·开本：16
·正文语种：英语
·丛书名：图灵原版数学·统计学系列
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内容简介《矩阵计算(英文版·第3版)》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。
《矩阵计算(英文版·第3版)》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。
作者简介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）。
编辑推荐《矩阵计算(英文版·第3版)》是由人民邮电出版社出版的。
目录
Matrix Multiplication Problems .
1.1 Basic Algorithms and Notation 2
1.2 Exploiting Structure 16
1.3 Block Matrices and Algorithms 24
1.4 Vectorization and Re-Use Issues 34
2 Matrix Analysis
2.1 Basic Ideas from Linear Algebra 48
2.2 Vector Norms 52
2.3 Matrix Norms 54
2.4 Finite Precision Matrix Computations 59
2.5 Orthogonality and the SVD 69
2.6 Projections and the CS Decomposition 75
2.7 The Sensitivity of Square Linear Systems 80
3 General Linear Systems
3.1 Triangular Systems 88
3.2 The LU Factorization 94
3.3 Roundoff Analysis of Gaussian Elimination 104
3.4 Pivoting 109
3.5 Improving and Estimating Accuracy 123
4 Special Linear Systems
4.1 The LDMT and LDLT Factorizations 135
4.2 Positive Definite Systems 140
4.3 Banded Systems 152
4.4 Symmetric Indefinite Systems 161
4.5 Block Systems 174
4.6 Vandermonde Systems and the FFT 183
4.7 Toeplitz and Related Systems 193
5 Orthogonalization and Least Squares
5.1 Householder and Givens Matrices 208
5.2 The QR Factorization 223
5.3 The Full Rank LS Problem 236
5.4 Other Orthogonal Factorizations 248
5.5 The Rank Deficient LS Problem 256
5.6 Weighting and Iterative Improvement 264
5.7 Square and Underdetermined Systems 270
6 Parallel Matrix Computations
6.1 Basic Concepts 276
6.2 Matrix Multiplication 292
6.3 Factorizations 300
7 The Unsymmetric Eigenvalue Problem ..
7.1 Properties and Decompositions 310
7.2 Perturbation Theory 320
7.3 Power Iterations 330
7.4 The Hessenberg and Real Schur Forms 341
7.5 The Practical QR Algorithm 352
7.6 Invariant Subspace Computations 362
7.7 The QZ Method for Ax = λ Bx 375
8 The Symmetric Eigenvalue Problem
8.1 Properties and Decompositions
8.2 Power Iterations 405
8.3 The Symmetric QR Algorithm 414
8.4 Jacobi Methods 426
8.5 Tridiagonal Methods 439
8.6 Computing the SVD 448
8.7 Some Generalized Eigenvalue Problems 461
9 Lanczos Methods
9.1 Derivation and Convergence Properties 471
9.2 Practical Lanczos Procedures 479
9.3 Applications to Ax = b and Least Squares 490
9.4 Arnoldi and Unsymmetric Lanczos 499
10 Iterative Methods for Linear Systems
10.1 The Standard Iterations 509
10.2 The Conjugate Gradient Method 520
10.3 Preconditioned Conjugate Gradients 532
10.4 Other Krylov Subspace Methods 544
11 Functions of Matrices
11.1 Eigenvalue Methods 556
11.2 Approximation Methods 562
11.3 The Matrix Exponential 572
12 Special Topics
12.1 Constrained Least Squares 580
12.2 Subset Selection Using the SVD 590
12.3 Total Least Squares 595
12.4 Computing Subspaces with the SVD 601
12.5 Updating Matrix Factorizations 606
12.6 Modified/Structured Eigenproblems 621
Index 637
……[看更多目录]
序言The field of matfix computations continues to grow and mature.In the Third Edition we have added over 300 new references and 100 new problems.The LINPACK and EISPACK citations have bden replaced with appropriate pointers to LAPACK With key codes tabulated at the beginning of appropriate chapters.
In the first Edition and Second Edition we identified a small number of global refefences：Wilkinson（1965），Forsythe and Moler（1967），Stewart （1973），Hanson and Lawson（1974）and Parlett （1980）.These volumes are as important as ever to the research landscape，but there are some mag- nificent new textbooks and monographs on the scene.See The Litemture section that follows.
We continue as before With the practice of giving references at the end of each section and a master bibliography at the end of the book.
The earlier editions suffered from a large number of typographical errors and we are obliged to the dozens of readers who have brought these to our attention.Many corrections and clarifications have been made. Here are some specific highlights of the new edition.Chapter 1（Matrix Multiplication Problems）and Chapter 6（Parallel Matrix Computations） have been completely rewritten with less formality.We think that this facilitates the building of intuition for high performance computing and draws a better line between algorithm and implementation on the printed page.
In Chapter 2（Matrix Analysisl we expanded the treatment of CS de- composition and included a proof.The overview of floating point arithmetic has been brought up to date.In Chapter 4（Special Linear Systems） we embellished the Toeplitz section with connections to circulant matrices and the fast Fourier transform.A subsection on equilibrium systems has been included in our treatment of indefinite systems.
A more accurate rendition of the modified Gram.Schmidt process is oifered in Chapter 5 fOrthogonalization and Least Squares）.Chapter 8 （The Symmetric Eigenproblem）has been extensively rewritten and rear ranged SO as to minimize its dependence upon Chapter 7 fThe Unsymmetric Eigenproblem）.Indeed，the coupling between these two chapters is now so minimal that it is possible to read either one flrst.
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