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Direct Methods for Sparse Matrices$
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I. S. Duff, A. M. Erisman, and J. K. Reid

Print publication date: 2017

Print ISBN-13: 9780198508380

Published to Oxford Scholarship Online: April 2017

DOI: 10.1093/acprof:oso/9780198508380.001.0001

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(p.1) 1 Introduction
Direct Methods for Sparse Matrices

I. S. Duff

A. M. Erisman

J. K. Reid

Oxford University Press

The use of graph theory to ‘visualize’ the relationship between sparsity patterns and Gaussian elimination is introduced. The potential of significant savings from the exploitation of sparsity is illustrated by one example. The effect of computer hardware on efficient computation is discussed. Realization of sparsity means more than faster solutions; it affects the formulation of mathematical models and the feasibility of solving them.

Keywords:   Gaussian elimination, graph theory, exploitation of sparsity, Computer hardware, standard test problems

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