A new perturbation bound for the LDU factorization of diagonally dominant matrices

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dc.contributor.author Dailey, Megan
dc.contributor.author Martínez Dopico, Froilán César
dc.contributor.author Ye, Qiang
dc.date.accessioned 2015-12-03T12:15:45Z
dc.date.available 2015-12-03T12:15:45Z
dc.date.issued 2014-07
dc.identifier.bibliographicCitation SIAM Journal on Matrix Analysis and Applications, 35 (2014) 3, pp. 904-930.
dc.identifier.issn 1095-7162 (Online)
dc.identifier.issn 0895-4798 (Print)
dc.identifier.uri http://hdl.handle.net/10016/22065
dc.description.abstract This work introduces a new perturbation bound for the L factor of the LDU factorization of (row) diagonally dominant matrices computed via the column diagonal dominance pivoting strategy. This strategy yields L and U factors which are always well-conditioned and, so, the LDU factorization is guaranteed to be a rank-revealing decomposition. The new bound together with those for the D and U factors in [F. M. Dopico and P. Koev, Numer. Math., 119 (2011), pp. 337– 371] establish that if diagonally dominant matrices are parameterized via their diagonally dominant parts and off-diagonal entries, then tiny relative componentwise perturbations of these parameters produce tiny relative normwise variations of L and U and tiny relative entrywise variations of D when column diagonal dominance pivoting is used. These results will allow us to prove in a follow-up work that such perturbations also lead to strong perturbation bounds for many other problems involving diagonally dominant matrices.
dc.description.sponsorship Research supported in part by Ministerio de Economía y Competitividad of Spain under grant MTM2012-32542.
dc.format.extent 27
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Society for Industrial and Applied Mathematics
dc.rights © 2014, Society for Industrial and Applied Mathematics
dc.subject.other Accurate computations
dc.subject.other column diagonal dominance pivoting
dc.subject.other diagonally dominant matrices
dc.subject.other LDU factorization
dc.subject.other rank-revealing decomposition
dc.subject.other relative perturbation theory
dc.subject.other diagonally dominant parts
dc.title A new perturbation bound for the LDU factorization of diagonally dominant matrices
dc.type article
dc.description.status Publicado
dc.relation.publisherversion http://dx.doi.org/10.1137/13093858X
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1137/13093858X
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM-2012-32542
dc.type.version publishedVersion
dc.identifier.publicationfirstpage 904
dc.identifier.publicationissue 3
dc.identifier.publicationlastpage 930
dc.identifier.publicationtitle SIAM journal on matrix analysis and applications
dc.identifier.publicationvolume 35
dc.identifier.uxxi AR/0000015780
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