Block subspace expansions for eigenvalues and eigenvectors approximation

Autores
Arrieta Zuccalli, Francisco Jose; Massey, Pedro Gustavo; Stojanoff, Demetrio
Año de publicación
2025
Idioma
inglés
Tipo de recurso
documento de conferencia
Estado
versión publicada
Descripción
Let A ∈ Cn×n be an Hermitian matrix with eigenvalues λ1 ≥ . . . ≥ λn. Assume that λd > λd+1 for some d ≥ 1 and let X ⊂ Cn be the simple A-invariant d-dimensional subspace spanned by the eigenvectors of A associated with the biggest eigenvalues. Given an initial subspace V ⊂ Cn with dim V = r ≥ d, we search for expansions V + A(W0), where W0 ⊂ V is such that dimW0 ≤ d and such that the expanded subspace is closer to X than V. We show that there exist optimal W0, in the sense that θi(X, V + A(W0)) ≤ θi(V + A(W)) for every W ⊂ V with dimW ≤ d, where θi(X, S) denotes the i-th principal angle between X and S, for 1 ≤ i ≤ d ≤ dim S. We relate these optimal expansions to block Krylov subspaces and show that, under these conditions on A and X, the corresponding iterative sequence of subspaces constructed in this way approximates X arbitrarily well. We further introduce computable versions of this construction and compute several numerical examples to test their performance.
Fil: Arrieta Zuccalli, Francisco Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de la Plata. Facultad de Cs.exactas. Centro de Matematica de la Plata.; Argentina
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de la Plata. Facultad de Cs.exactas. Centro de Matematica de la Plata.; Argentina
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de la Plata. Facultad de Cs.exactas. Centro de Matematica de la Plata.; Argentina
X Congreso de Matemática Aplicada Computacional e Industrial
Córdoba
Argentina
Asociación Argentina de Matemática Aplicada, Computacional e Industrial
Materia
OPTIMAL SUBSPACE EXPANSION
EIGENVECTOR APPOXIMATION
BLOCK KRYLOV SUBSPACE
PROJECTION METHODS
COMPUTABLE SUBSPACE EXPANSION
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:11336/282456
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/282456
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Block subspace expansions for eigenvalues and eigenvectors approximationArrieta Zuccalli, Francisco JoseMassey, Pedro GustavoStojanoff, DemetrioOPTIMAL SUBSPACE EXPANSIONEIGENVECTOR APPOXIMATIONBLOCK KRYLOV SUBSPACEPROJECTION METHODSCOMPUTABLE SUBSPACE EXPANSIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let A ∈ Cn×n be an Hermitian matrix with eigenvalues λ1 ≥ . . . ≥ λn. Assume that λd > λd+1 for some d ≥ 1 and let X ⊂ Cn be the simple A-invariant d-dimensional subspace spanned by the eigenvectors of A associated with the biggest eigenvalues. Given an initial subspace V ⊂ Cn with dim V = r ≥ d, we search for expansions V + A(W0), where W0 ⊂ V is such that dimW0 ≤ d and such that the expanded subspace is closer to X than V. We show that there exist optimal W0, in the sense that θi(X, V + A(W0)) ≤ θi(V + A(W)) for every W ⊂ V with dimW ≤ d, where θi(X, S) denotes the i-th principal angle between X and S, for 1 ≤ i ≤ d ≤ dim S. We relate these optimal expansions to block Krylov subspaces and show that, under these conditions on A and X, the corresponding iterative sequence of subspaces constructed in this way approximates X arbitrarily well. We further introduce computable versions of this construction and compute several numerical examples to test their performance.Fil: Arrieta Zuccalli, Francisco Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de la Plata. Facultad de Cs.exactas. Centro de Matematica de la Plata.; ArgentinaFil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de la Plata. Facultad de Cs.exactas. Centro de Matematica de la Plata.; ArgentinaFil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de la Plata. Facultad de Cs.exactas. Centro de Matematica de la Plata.; ArgentinaX Congreso de Matemática Aplicada Computacional e IndustrialCórdobaArgentinaAsociación Argentina de Matemática Aplicada, Computacional e IndustrialAsociación Argentina de Matemática Aplicada, Computacional e Industrial2025info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObjectCongresoJournalhttp://purl.org/coar/resource_type/c_5794info:ar-repo/semantics/documentoDeConferenciaapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/282456Block subspace expansions for eigenvalues and eigenvectors approximation; X Congreso de Matemática Aplicada Computacional e Industrial; Córdoba; Argentina; 2025; 52-552314-3282CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://asamaci.org.ar/revista-maci/Nacionalinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2026-03-11T12:30:15Zoai:ri.conicet.gov.ar:11336/282456instacron: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:34982026-03-11 12:30:15.946CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Block subspace expansions for eigenvalues and eigenvectors approximation
title Block subspace expansions for eigenvalues and eigenvectors approximation
spellingShingle Block subspace expansions for eigenvalues and eigenvectors approximation
Arrieta Zuccalli, Francisco Jose
OPTIMAL SUBSPACE EXPANSION
EIGENVECTOR APPOXIMATION
BLOCK KRYLOV SUBSPACE
PROJECTION METHODS
COMPUTABLE SUBSPACE EXPANSION
title_short Block subspace expansions for eigenvalues and eigenvectors approximation
title_full Block subspace expansions for eigenvalues and eigenvectors approximation
title_fullStr Block subspace expansions for eigenvalues and eigenvectors approximation
title_full_unstemmed Block subspace expansions for eigenvalues and eigenvectors approximation
title_sort Block subspace expansions for eigenvalues and eigenvectors approximation
dc.creator.none.fl_str_mv Arrieta Zuccalli, Francisco Jose
Massey, Pedro Gustavo
Stojanoff, Demetrio
author Arrieta Zuccalli, Francisco Jose
author_facet Arrieta Zuccalli, Francisco Jose
Massey, Pedro Gustavo
Stojanoff, Demetrio
author_role author
author2 Massey, Pedro Gustavo
Stojanoff, Demetrio
author2_role author
author
dc.subject.none.fl_str_mv OPTIMAL SUBSPACE EXPANSION
EIGENVECTOR APPOXIMATION
BLOCK KRYLOV SUBSPACE
PROJECTION METHODS
COMPUTABLE SUBSPACE EXPANSION
topic OPTIMAL SUBSPACE EXPANSION
EIGENVECTOR APPOXIMATION
BLOCK KRYLOV SUBSPACE
PROJECTION METHODS
COMPUTABLE SUBSPACE EXPANSION
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 ∈ Cn×n be an Hermitian matrix with eigenvalues λ1 ≥ . . . ≥ λn. Assume that λd > λd+1 for some d ≥ 1 and let X ⊂ Cn be the simple A-invariant d-dimensional subspace spanned by the eigenvectors of A associated with the biggest eigenvalues. Given an initial subspace V ⊂ Cn with dim V = r ≥ d, we search for expansions V + A(W0), where W0 ⊂ V is such that dimW0 ≤ d and such that the expanded subspace is closer to X than V. We show that there exist optimal W0, in the sense that θi(X, V + A(W0)) ≤ θi(V + A(W)) for every W ⊂ V with dimW ≤ d, where θi(X, S) denotes the i-th principal angle between X and S, for 1 ≤ i ≤ d ≤ dim S. We relate these optimal expansions to block Krylov subspaces and show that, under these conditions on A and X, the corresponding iterative sequence of subspaces constructed in this way approximates X arbitrarily well. We further introduce computable versions of this construction and compute several numerical examples to test their performance.
Fil: Arrieta Zuccalli, Francisco Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de la Plata. Facultad de Cs.exactas. Centro de Matematica de la Plata.; Argentina
Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de la Plata. Facultad de Cs.exactas. Centro de Matematica de la Plata.; Argentina
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de la Plata. Facultad de Cs.exactas. Centro de Matematica de la Plata.; Argentina
X Congreso de Matemática Aplicada Computacional e Industrial
Córdoba
Argentina
Asociación Argentina de Matemática Aplicada, Computacional e Industrial
description Let A ∈ Cn×n be an Hermitian matrix with eigenvalues λ1 ≥ . . . ≥ λn. Assume that λd > λd+1 for some d ≥ 1 and let X ⊂ Cn be the simple A-invariant d-dimensional subspace spanned by the eigenvectors of A associated with the biggest eigenvalues. Given an initial subspace V ⊂ Cn with dim V = r ≥ d, we search for expansions V + A(W0), where W0 ⊂ V is such that dimW0 ≤ d and such that the expanded subspace is closer to X than V. We show that there exist optimal W0, in the sense that θi(X, V + A(W0)) ≤ θi(V + A(W)) for every W ⊂ V with dimW ≤ d, where θi(X, S) denotes the i-th principal angle between X and S, for 1 ≤ i ≤ d ≤ dim S. We relate these optimal expansions to block Krylov subspaces and show that, under these conditions on A and X, the corresponding iterative sequence of subspaces constructed in this way approximates X arbitrarily well. We further introduce computable versions of this construction and compute several numerical examples to test their performance.
publishDate 2025
dc.date.none.fl_str_mv 2025
dc.type.none.fl_str_mv info:eu-repo/semantics/publishedVersion
info:eu-repo/semantics/conferenceObject
Congreso
Journal
http://purl.org/coar/resource_type/c_5794
info:ar-repo/semantics/documentoDeConferencia
status_str publishedVersion
format conferenceObject
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/282456
Block subspace expansions for eigenvalues and eigenvectors approximation; X Congreso de Matemática Aplicada Computacional e Industrial; Córdoba; Argentina; 2025; 52-55
2314-3282
CONICET Digital
CONICET
url http://hdl.handle.net/11336/282456
identifier_str_mv Block subspace expansions for eigenvalues and eigenvectors approximation; X Congreso de Matemática Aplicada Computacional e Industrial; Córdoba; Argentina; 2025; 52-55
2314-3282
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://asamaci.org.ar/revista-maci/
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.coverage.none.fl_str_mv Nacional
dc.publisher.none.fl_str_mv Asociación Argentina de Matemática Aplicada, Computacional e Industrial
publisher.none.fl_str_mv Asociación Argentina de Matemática Aplicada, Computacional e Industrial
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 12.977003

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