Direct Methods for Sparse Matrices

by Duff, I. S.; Erisman, A. M.; Reid, J. K.

• ISBN13: 9780198534211
• ISBN10: 0198534213
• Edition: Reprint
• Format: Paperback
• Copyright: 1989-08-24
• Publisher: Clarendon Press

Summary

This book provides practical approaches to the efficient use of sparsity--a key to solving large problems in many fields, including computational science and engineering, where mathematical models give rise to very large systems of linear equations. The emphasis is on practicality, with conclusions based on concrete experience. Non-numeric computing techniques have been included as well as frequent illustrations in an attempt to bridge the gap between the written word and the working computer code. Exercises have been included to strengthen understanding of the material as well as to extend it for students and researchers in engineering, mathematics, and computer science.

Table of Contents

Introduction

Sparse matrices: storage schemes and simple operations

Gaussian elimination for dense matrices: the algebraic approach

Gaussian elimination for dense matrices: numerical considerations

Gaussian elimination for sparse matrices: an introduction

Reduction to block triangular form

Local pivotal strategies for sparse matrices

Ordering sparse matrices to special forms

Implementing Gaussian elimination: ANALYSE with numerical values

Implementing Gaussian elimination with symbolic ANALYSE

Partitioning, matrix modification, and tearing

Other sparsity-oriented issues

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