Relative perturbation theory for 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 2015-12-04T09:20:40Z
dc.date.available 2015-12-04T09:20:40Z
dc.date.issued 2014-10
dc.identifier.bibliographicCitation SIAM Journal on Matrix Analysis and Applications, 35 (2014), pp. 1303-1328.
dc.identifier.issn 0895-4798 (Print)
dc.identifier.issn 1095-7162 (Online)
dc.identifier.uri http://hdl.handle.net/10016/22068
dc.description.abstract In this paper, strong relative perturbation bounds are developed for a number of linear algebra problems involving diagonally dominant matrices. The key point is to parameterize diagonally dominant matrices using their off-diagonal entries and diagonally dominant parts and to consider small relative componentwise perturbations of these parameters. This allows us to obtain new relative perturbation bounds for the inverse, the solution to linear systems, the symmetric indefinite eigenvalue problem, the singular value problem, and the nonsymmetric eigenvalue problem. These bounds are much stronger than traditional perturbation results, since they are independent of either the standard condition number or the magnitude of eigenvalues/singular values. Together with previously derived perturbation bounds for the LDU factorization and the symmetric positive definite eigenvalue problem, this paper presents a complete and detailed account of relative structured perturbation theory for diagonally dominant matrices.
dc.description.sponsorship This research was partially supported by the Ministerio de Economía y Competitividad of Spain under grant MTM2012-32542.
dc.format.extent 26
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 Diagonally dominant matrices
dc.subject.other Diagonally dominant parts
dc.subject.other Eigenvalues
dc.subject.other Inverses
dc.subject.other Linear systems
dc.subject.other Relative perturbation theory
dc.subject.other Singular values
dc.subject.other Eigenvalues and eigenfunctions
dc.subject.other Inverse problems
dc.subject.other Matrix algebra
dc.subject.other Number theory
dc.subject.other Perturbation techniques.
dc.title Relative perturbation theory for diagonally dominant matrices
dc.type article
dc.description.status Publicado
dc.relation.publisherversion http://dx.doi.org/10.1137/130943613
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1137/130943613
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM-2012-32542
dc.type.version publishedVersion
dc.identifier.publicationfirstpage 1303
dc.identifier.publicationissue 4
dc.identifier.publicationlastpage 1328
dc.identifier.publicationtitle SIAM Journal on Matrix Analysis and Applications
dc.identifier.publicationvolume 35
dc.identifier.uxxi AR/0000016029
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