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Matrix Algorithms Vol. 1 : Basic Decompositions by G. W. Stewart (1998, Trade Paperback)

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About this product

Product Identifiers

PublisherSociety for Industrial AND Applied Mathematics

ISBN-100898714141

ISBN-139780898714142

eBay Product ID (ePID)221267

Product Key Features

Number of Pages476 Pages

LanguageEnglish

Publication NameMatrix Algorithms Vol. 1 : Basic Decompositions

SubjectMatrices, Mathematical Analysis

Publication Year1998

TypeTextbook

Subject AreaMathematics

AuthorG. W. Stewart

FormatTrade Paperback

Dimensions

Item Height1.1 in

Item Weight36 Oz

Item Length11.3 in

Item Width7.1 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN98-022445

Dewey Edition21

IllustratedYes

Volume NumberVol. 1

Dewey Decimal512.9/434

Table Of ContentAlgorithms Notation Preface Chapter 1: Matrices, Algebra, and Analysis. Vectors Matrices Linear Algebra Analysis Addenda Chapter 2: Matrices and Machines. Pseudocode Triangular Systems Matrices in Memory Rounding Error Chapter 3: Gaussian Elimination. Gaussian Elimination A Most Versatile Algorithm The Sensitivity of Linear Systems The Effects of Rounding Error Chapter 4: The QR Decomposition and Least Squares. The QR Decomposition Linear Least Squares Updating Chapter 5: Rank-Reducing Decompositions. Fundamental Subspaces and Rank Estimation Pivoted Orthogonal Triangularization Norm and Condition Estimation UTV Decompositions References Index.

SynopsisThis thorough, concise, and superbly written volume is the first in a self-contained five-volume series devoted to matrix algorithms. It focuses on the computation of matrix decompositions - the factorization of matrices into products of similar ones. The first two chapters provide the required background from mathematics and computer science needed to work effectively in matrix computations. The remaining chapters are devoted to the computation and applications of the LU and QR decompositions. The series is aimed at the nonspecialist who needs more than black-box proficiency with matrix computations. A certain knowledge of elementary analysis and linear algebra is assumed, as well as a reasonable amount of programming experience. The guiding principle, that if something is worth explaining, it is worth explaining fully, has necessarily restricted the scope of the series, but the selection of topics should give the reader a sound basis for further study., This thorough, concise, and superbly written volume is the first in a self-contained five-volume series devoted to matrix algorithms. It focuses on the computation of matrix decompositions-that is, the factorization of matrices into products of similar ones., This thorough, concise, and superbly written volume is the first in a self-contained five-volume series devoted to matrix algorithms. It focuses on the computation of matrix decompositions-that is, the factorization of matrices into products of similar ones. The first two chapters provide the required background from mathematics and computer science needed to work effectively in matrix computations. The remaining chapters are devoted to the LU and QR decompositions-their computation and applications. The singular value decomposition is also treated, although algorithms for its computation will appear in the second volume of the series. The present volume contains 65 algorithms formally presented in pseudocode. Other volumes in the series will treat eigensystems, iterative methods, sparse matrices, and structured problems. The series is aimed at the nonspecialist who needs more than black-box proficiency with matrix computations. To give the series focus, the emphasis is on algorithms, their derivation, and their analysis. The reader is assumed to have a knowledge of elementary analysis and linear algebra and a reasonable amount of programming experience, typically that of the beginning graduate engineer or the undergraduate in an honors program. Strictly speaking, the individual volumes are not textbooks, although they are intended to teach, the guiding principle being that if something is worth explaining, it is worth explaining fully. This has necessarily restricted the scope of the series, but the selection of topics should give the reader a sound basis for further study.

LC Classification NumberQA188 .S714 1998