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dc.contributor.author
Contino, Maximiliano
dc.contributor.author
Giribet, Juan Ignacio
dc.contributor.author
Maestripieri, Alejandra Laura
dc.date.available
2018-11-28T20:40:05Z
dc.date.issued
2017-04
dc.identifier.citation
Contino, Maximiliano; Giribet, Juan Ignacio; Maestripieri, Alejandra Laura; Weighted least squares solutions of the equation AXB - C = 0; Elsevier Science Inc; Linear Algebra and its Applications; 518; 4-2017; 177-197
dc.identifier.issn
0024-3795
dc.identifier.uri
http://hdl.handle.net/11336/65550
dc.description.abstract
Let H be a Hilbert space, L(H) the algebra of bounded linear operators on H and W ∈ L(H) a positive operator such that W^1/2 is in the p-Schatten class, for some 1 ≤ p < ∞. Given A,B ∈ L(H) with closed range and C ∈ L(H), we study the following weighted approximation problem: analyze the existence ofmin{ ||AXB − C||p,W , X ∈L(H)}, (0.1)where ||X ||p,W = ||W^1/2 X ||p . We also study the related operator approximation problem: analyze the existence ofmin {(AXB − C)*W (AXB − C), X ∈L(H)}, (0.2)where the order is the one induced in L(H) by the cone of positive operators. In this paper we prove that the existence of the minimum of (0.2) is equivalent to the existence of a solution of the normal equation A*W (AXB − C) = 0. We also give sufficient conditions for the existence of the minimum.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Elsevier Science Inc
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.subject
Oblique Projections
dc.subject
Operator Approximation
dc.subject
Schatten P Classes
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Weighted least squares solutions of the equation AXB - C = 0
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2018-11-12T13:21:46Z
dc.identifier.eissn
1873-1856
dc.journal.volume
518
dc.journal.pagination
177-197
dc.journal.pais
Estados Unidos
dc.description.fil
Fil: Contino, Maximiliano. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
dc.description.fil
Fil: Giribet, Juan Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
dc.description.fil
Fil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
dc.journal.title
Linear Algebra and its Applications
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0024379516306279
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1016/j.laa.2016.12.028
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1610.00645


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