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Gaussian elimination for dense matrices: the algebraic problem

I. S. Duff, A. M. Erisman, and J. K. Reid

in Direct Methods for Sparse Matrices

Published in print:
2017
Published Online:
April 2017
ISBN:
9780198508380
eISBN:
9780191746420
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508380.003.0003
Subject:
Mathematics, Numerical Analysis

We review the fundamental operations in the direct solution of linear equations without concern for rounding error caused by computer arithmetic. We consider the relationship between Gaussian ... More


Local pivotal strategies for sparse matrices

I. S. Duff, A. M. Erisman, and J. K. Reid

in Direct Methods for Sparse Matrices

Published in print:
2017
Published Online:
April 2017
ISBN:
9780198508380
eISBN:
9780191746420
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508380.003.0007
Subject:
Mathematics, Numerical Analysis

We consider local strategies for pivot selection, that is, where decisions are made at each stage of the factorization without regard to how they might affect later stages. They include minimum ... More


The solve phase

I. S. Duff, A. M. Erisman, and J. K. Reid

in Direct Methods for Sparse Matrices

Published in print:
2017
Published Online:
April 2017
ISBN:
9780198508380
eISBN:
9780191746420
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508380.003.0014
Subject:
Mathematics, Numerical Analysis

We examine the SOLVE phase in the direct solution of sparse systems. Here we assume that the factors have been computed and we study the efficient use of these to determine the solution through ... More


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