矩阵计算

前言

　　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.

内容概要

Gene H. Golub (1932－2007)  美国科学院、工程院和艺术科学院院士，世界著名的数值分析专家，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（Singular Value 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（International Congress on Industrial and Applied Mathematics, ICIAM）。

Charles F. Van Loan  著名数值分析专家。美国康奈尔大学教授，曾任该校计算机科学系主任。他于1973年在密歇根大学获得博士学位，师从Cleve Moler。

书籍目录

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　

作者简介

本书是国际上数值计算方面的权威著作，有“圣经”之称。被美国加州大学、斯坦福大学、华盛顿大学、芝加哥大学、中国科学院研究生院等很多世界知名学府用作相关课程的教材或主要参考书。

本书系统地介绍了矩阵计算的基本理论和方法。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，非常有助于自学。

图书封面

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