Matrix algorithms. Vol. 1, Basic decompositions / G.W. Stewart.

Format:

Book

Author/Creator:

Stewart, G. W. (Gilbert W.)

Contributor:

Society for Industrial and Applied Mathematics.

Language:

English

Subjects (All):

Matrices.

Physical Description:

1 electronic text (xix, 458 p.) : ill., digital file.

Other Title:

Basic decompositions.

Place of Publication:

Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1998.

Language Note:

English

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

This 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.

Contents:

Algorithms

Notation

Preface

Chapter 1. Matrices, algebra, and analysis

Chapter 2. Matrices and machines

Chapter 3. Gaussian elimination

Chapter 4. The QR decomposition and least squares

Chapter 5. Rank-reducing decompositions

References

Index.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Title from title screen, viewed 04/05/2011.

ISBN:

1-61197-140-3

Publisher Number:

OT60 SIAM