Matrix Algorithms Volume I: Basic Decompositions

✍ Scribed by G. W. Stewart

• Year: 1998
• Tongue: English
• Leaves: 479
• Edition: 1
• Category: Library

✦ Synopsis

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 - 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.

✦ Table of Contents

Matrix Algorithms......Page 2
Volume I: Basic Decompositions......Page 4
ISBN 0-89871-414-1......Page 5
Contents......Page 6
Algorithms......Page 14
Notation......Page 16
Preface......Page 18
1 Matrices, Algebra, and Analysis......Page 22
2 Matrices and Machines......Page 102
3 Gaussian Elimination......Page 168
4 The QR Decomposition and Least Squares......Page 270
5 Rank-Reducing Decompositions......Page 378
References......Page 438
Index......Page 462