Absolute Variation of Ritz Values, Principal Angles, and Spectral Spread

Autores
Massey, Pedro Gustavo; Stojanoff, Demetrio; Zarate, Sebastian Gonzalo
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let A be a d×d complex self-adjoint matrix, X,Y⊂Cd be k-dimensional subspaces and let X be a d×k complex matrix whose columns form an orthonormal basis of X. We construct a d×k complex matrix Yr whose columns form an orthonormal basis of Y and obtain sharp upper bounds for the singular values s(X∗AX−Y∗rAYr) in terms of submajorization relations involving the principal angles between X and Y and the spectral spread of A. We apply these results to obtain sharp upper bounds for the absolute variation of the Ritz values of A associated with the subspaces X and Y, that partially confirm conjectures by Knyazev and Argentati.
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Zarate, Sebastian Gonzalo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Materia
PRINCIPAL ANGLES
RITZ VALUES
SPECTRAL SPREAD
MAJORIZATION
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/150979
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Absolute Variation of Ritz Values, Principal Angles, and Spectral SpreadMassey, Pedro GustavoStojanoff, DemetrioZarate, Sebastian GonzaloPRINCIPAL ANGLESRITZ VALUESSPECTRAL SPREADMAJORIZATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let A be a d×d complex self-adjoint matrix, X,Y⊂Cd be k-dimensional subspaces and let X be a d×k complex matrix whose columns form an orthonormal basis of X. We construct a d×k complex matrix Yr whose columns form an orthonormal basis of Y and obtain sharp upper bounds for the singular values s(X∗AX−Y∗rAYr) in terms of submajorization relations involving the principal angles between X and Y and the spectral spread of A. We apply these results to obtain sharp upper bounds for the absolute variation of the Ritz values of A associated with the subspaces X and Y, that partially confirm conjectures by Knyazev and Argentati.Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Zarate, Sebastian Gonzalo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaSociety for Industrial and Applied Mathematics2021-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/150979Massey, Pedro Gustavo; Stojanoff, Demetrio; Zarate, Sebastian Gonzalo; Absolute Variation of Ritz Values, Principal Angles, and Spectral Spread; Society for Industrial and Applied Mathematics; Siam Journal On Matrix Analysis And Applications; 42; 4; 10-2021; 1506-15270895-47981095-7162CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://epubs.siam.org/doi/10.1137/20M1386906info:eu-repo/semantics/altIdentifier/doi/10.1137/20M1386906info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2012.09018info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T09:56:46Zoai:ri.conicet.gov.ar:11336/150979instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-11-05 09:56:47.12CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Absolute Variation of Ritz Values, Principal Angles, and Spectral Spread
title Absolute Variation of Ritz Values, Principal Angles, and Spectral Spread
spellingShingle Absolute Variation of Ritz Values, Principal Angles, and Spectral Spread
Massey, Pedro Gustavo
PRINCIPAL ANGLES
RITZ VALUES
SPECTRAL SPREAD
MAJORIZATION
title_short Absolute Variation of Ritz Values, Principal Angles, and Spectral Spread
title_full Absolute Variation of Ritz Values, Principal Angles, and Spectral Spread
title_fullStr Absolute Variation of Ritz Values, Principal Angles, and Spectral Spread
title_full_unstemmed Absolute Variation of Ritz Values, Principal Angles, and Spectral Spread
title_sort Absolute Variation of Ritz Values, Principal Angles, and Spectral Spread
dc.creator.none.fl_str_mv Massey, Pedro Gustavo
Stojanoff, Demetrio
Zarate, Sebastian Gonzalo
author Massey, Pedro Gustavo
author_facet Massey, Pedro Gustavo
Stojanoff, Demetrio
Zarate, Sebastian Gonzalo
author_role author
author2 Stojanoff, Demetrio
Zarate, Sebastian Gonzalo
author2_role author
author
dc.subject.none.fl_str_mv PRINCIPAL ANGLES
RITZ VALUES
SPECTRAL SPREAD
MAJORIZATION
topic PRINCIPAL ANGLES
RITZ VALUES
SPECTRAL SPREAD
MAJORIZATION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let A be a d×d complex self-adjoint matrix, X,Y⊂Cd be k-dimensional subspaces and let X be a d×k complex matrix whose columns form an orthonormal basis of X. We construct a d×k complex matrix Yr whose columns form an orthonormal basis of Y and obtain sharp upper bounds for the singular values s(X∗AX−Y∗rAYr) in terms of submajorization relations involving the principal angles between X and Y and the spectral spread of A. We apply these results to obtain sharp upper bounds for the absolute variation of the Ritz values of A associated with the subspaces X and Y, that partially confirm conjectures by Knyazev and Argentati.
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Zarate, Sebastian Gonzalo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
description Let A be a d×d complex self-adjoint matrix, X,Y⊂Cd be k-dimensional subspaces and let X be a d×k complex matrix whose columns form an orthonormal basis of X. We construct a d×k complex matrix Yr whose columns form an orthonormal basis of Y and obtain sharp upper bounds for the singular values s(X∗AX−Y∗rAYr) in terms of submajorization relations involving the principal angles between X and Y and the spectral spread of A. We apply these results to obtain sharp upper bounds for the absolute variation of the Ritz values of A associated with the subspaces X and Y, that partially confirm conjectures by Knyazev and Argentati.
publishDate 2021
dc.date.none.fl_str_mv 2021-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/150979
Massey, Pedro Gustavo; Stojanoff, Demetrio; Zarate, Sebastian Gonzalo; Absolute Variation of Ritz Values, Principal Angles, and Spectral Spread; Society for Industrial and Applied Mathematics; Siam Journal On Matrix Analysis And Applications; 42; 4; 10-2021; 1506-1527
0895-4798
1095-7162
CONICET Digital
CONICET
url http://hdl.handle.net/11336/150979
identifier_str_mv Massey, Pedro Gustavo; Stojanoff, Demetrio; Zarate, Sebastian Gonzalo; Absolute Variation of Ritz Values, Principal Angles, and Spectral Spread; Society for Industrial and Applied Mathematics; Siam Journal On Matrix Analysis And Applications; 42; 4; 10-2021; 1506-1527
0895-4798
1095-7162
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://epubs.siam.org/doi/10.1137/20M1386906
info:eu-repo/semantics/altIdentifier/doi/10.1137/20M1386906
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2012.09018
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.087074

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