矩陣計(jì)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），F(xiàn)orsythe 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.

內(nèi)容概要

本書系統(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)后還附有習(xí)題，并有注釋和大量參考文獻(xiàn)?！　”緯勺鳛楦叩葘W(xué)校數(shù)學(xué)系高年級(jí)本科生和研究生的教材，亦可作為計(jì)算數(shù)學(xué)和工程技術(shù)人員的參考用書。

作者簡介

Gene H.Golub，（1932-2007），美國科學(xué)院、工程院和藝術(shù)科學(xué)院院士，世界著名的數(shù)分析專家，現(xiàn)代矩陣計(jì)算的奠基人，生前曾任斯坦福大學(xué)教授。他是矩陣分解算法的主要貢獻(xiàn)者，與William Kahan在1970年給出了奇異值分解（SingularValue Decomposition,SVD）的可行算法，一直沿用至今。他發(fā)起組織了工業(yè)與應(yīng)用數(shù)學(xué)國際會(huì)議（Intemational Congress on Industrial and Applied Mathematics，ICIAM）。

書籍目錄

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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