On the existence and computation of rank-revealing LU factorizations
type: Item
instance of: scholarly article
title: On the existence and computation of rank-revealing LU factorizations
zbMATH Open document ID: 0962.65023
DOI: 10.1016/S0024-3795(00)00120-8
author: R. Smith
published in: Linear Algebra and its Applications
publication date: 2001-05-31T00:00:00Z
review text: Exploring the properties of Schur complements, an existence theory for LU factorizations, which is similar to that of rank-revealing QR factorizations, is given. Two algorithms are proposed. Both use Gaussian elimination with a block pivoting technique to select, from the coefficient matrix, a subset of columns each with guaranteed relatively large smallest singular value. Each of the proposed algorithms, for dense matrices, is faster than its orthogonal counterpart. Based on these two algorithms, an algorithm using only Gaussian elimination for computing rank-revealing LU factorizations is introduced. Results of computational experiments are given.
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65F20
zbMATH DE Number: 1533001
zbMATH Keywords: rank revealing LU factorization
zbMATH Keywords: singular values
zbMATH Keywords: Schur complements
zbMATH Keywords: algorithms
zbMATH Keywords: Gaussian elimination
zbMATH Keywords: block pivoting
reviewed by: R. P. Tewarson
describes a project that uses: RRQR
describes a project that uses: toms/782
MaRDI profile type: Publication
Wikidata QID: Q114122594
cites work: A volume associated with \(m{\times}n\) matrices
cites work: Algorithm 782
cites work: Computing rank-revealing QR factorizations of dense matrices
cites work: On the Existence and Computation of LU-Factorizations with Small Pivots
cites work: On Rank-Revealing Factorisations
cites work: Manifestations of the Schur complement
cites work: Q4348513
cites work: Q3359644
cites work: A theory of pseudoskeleton approximations
cites work: Efficient Algorithms for Computing a Strong Rank-Revealing QR Factorization
cites work: Q5753437
cites work: Rank-Revealing QR Factorizations and the Singular Value Decomposition
cites work: Matrix Analysis
cites work: Improved bound for rank revealing LU factorizations
cites work: Rank revealing \(LU\) factorizations
cites work: Q4841325
cites work: Bounds on singular values revealed by QR factorizations
cites work: The least squares problem and pseudo-inverses
cites work: Q4220521
description: scientific article; zbMATH DE number 1533001