Multiplicative perturbation theory of the Moore-Penrose inverse and the least squares problem

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Show simple item record Castro Gonzalez, Nieves Martínez Dopico, Froilán César Molera Molera, Juan Manuel 2021-04-07T09:00:15Z 2021-04-07T09:00:15Z 2016-08-15
dc.identifier.bibliographicCitation Castro-González, N., Dopico, F. M. & Molera, J. M. (2016). Multiplicative perturbation theory of the Moore–Penrose inverse and the least squares problem. Linear Algebra and Its Applications, 503, pp. 1–25.
dc.identifier.issn 0024-3795
dc.description.abstract Bounds for the variation of the Moore Penrose inverse of general matrices under multiplicative perturbations are presented. Their advantages with respect to classical bounds under additive perturbations and with respect to other bounds under multiplicative perturbations available in the literature are carefully studied and established. Closely connected to these developments a complete multiplicative perturbation theory for least squares problems, valid for perturbations of any size, is also presented, improving in this way recent multiplicative perturbation bounds which are valid only to first order in the size of the perturbations. The results in this paper are mainly based on exact expressions of the perturbed Moore-Penrose inverse in terms of the unperturbed one, the perturbation matrices, and certain orthogonal projectors. Such feature makes the new results amenable to be generalized in the future to linear operators in infinite dimensional spaces.
dc.format.extent 25
dc.language.iso eng
dc.publisher Elsevier
dc.rights © 2016 Elsevier Inc.
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.subject.other Least squares problems
dc.subject.other Moore-penrose inverse
dc.subject.other Multiplicative perturbation theory
dc.subject.other Accurate
dc.title Multiplicative perturbation theory of the Moore-Penrose inverse and the least squares problem
dc.type article
dc.subject.eciencia Matemáticas
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2015-68805-REDT
dc.relation.projectID Gobierno de España. MTM2012-32542
dc.relation.projectID Gobierno de España. MTM2015-65798-P
dc.relation.projectID Gobierno de España. MTM2010-18057
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 1
dc.identifier.publicationlastpage 25
dc.identifier.publicationtitle Linear Algebra and Its Applications
dc.identifier.publicationvolume 503
dc.identifier.uxxi AR/0000018084
dc.contributor.funder Ministerio de Economía y Competitividad (España)
dc.contributor.funder Ministerio de Ciencia e Innovación (España)
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