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LU factoring of non-invertible matrices

LU factoring of non-invertible matrices The definition of the LU factoring of a matrix usually requires that the matrix be invertible. Current software systems have extended the definition to non-square and rank-deficient matrices, but each has chosen a different extension. Two new extensions, both of which could serve as useful standards, are proposed here: the first combines LU factoring with full-rank factoring, and the second extension combines full-rank factoring with fraction-free methods. Amongst other applications, the extension to full-rank, fraction-free factoring is the basis for a fractionfree computation of the Moore-Penrose inverse. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM SIGSAM Bulletin Association for Computing Machinery

LU factoring of non-invertible matrices

ACM SIGSAM Bulletin , Volume 44 (1/2) – Jul 29, 2010

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References (40)

Publisher
Association for Computing Machinery
Copyright
The ACM Portal is published by the Association for Computing Machinery. Copyright © 2010 ACM, Inc.
Subject
Algebraic algorithms
ISSN
0163-5824
DOI
10.1145/1838599.1838602
Publisher site
See Article on Publisher Site

Abstract

The definition of the LU factoring of a matrix usually requires that the matrix be invertible. Current software systems have extended the definition to non-square and rank-deficient matrices, but each has chosen a different extension. Two new extensions, both of which could serve as useful standards, are proposed here: the first combines LU factoring with full-rank factoring, and the second extension combines full-rank factoring with fraction-free methods. Amongst other applications, the extension to full-rank, fraction-free factoring is the basis for a fractionfree computation of the Moore-Penrose inverse.

Journal

ACM SIGSAM BulletinAssociation for Computing Machinery

Published: Jul 29, 2010

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