PHIDE: A Parallel Hybrid Direct-Iterative Eigensolver for Hermitian Eigenvalue Problems

[EN] In this paper, we propose a Parallel Hybrid Direct-Iterative Eigensolver for Hermitian Eigenvalue Problems without tridiagonalization, denoted by PHIDE, which combines direct and iterative methods. PHIDE first reduces a Hermitian matrix to banded form, then applies a spectrum slicing algorithm...

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Detalles Bibliográficos
Autores: Li, Shengguo, Wu, Xinzhe, Yuan, Ziyang, Wang, Ruibo, Li, Tiejun, Xie, Yi, Yang, Bo, Chen, Xuguang, Jose E. Roman|||0000-0003-1144-6772
Tipo de recurso: artículo
Fecha de publicación:2026
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/231178
Acceso en línea:https://riunet.upv.es/handle/10251/231178
Access Level:acceso abierto
Palabra clave:Eigenvalues
Spectrum-slicing algorithms
Banded matrices
Direct eigenvalue methods
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spelling PHIDE: A Parallel Hybrid Direct-Iterative Eigensolver for Hermitian Eigenvalue ProblemsLi, ShengguoWu, XinzheYuan, ZiyangWang, RuiboLi, TiejunXie, YiYang, BoChen, XuguangJose E. Roman|||0000-0003-1144-6772EigenvaluesSpectrum-slicing algorithmsBanded matricesDirect eigenvalue methods[EN] In this paper, we propose a Parallel Hybrid Direct-Iterative Eigensolver for Hermitian Eigenvalue Problems without tridiagonalization, denoted by PHIDE, which combines direct and iterative methods. PHIDE first reduces a Hermitian matrix to banded form, then applies a spectrum slicing algorithm to the banded matrix, and finally computes the eigenvectors of the original matrix via backtransformation. Compared with conventional direct eigensolvers, PHIDE avoids tridiagonalization, which involves many memory-bound operations. In PHIDE, the banded eigenvalue problem is solved using the contour integral method implemented in FEAST, which may yield slightly lower accuracy than tridiagonalization-based approaches. For sequences of correlated Hermitian eigenvalue problems arising in density functional theory (DFT), PHIDE achieves an average speedup of 1.22x over the state-of-the-art direct solver in ELPA when using 1024 processes. Numerical experiments are conducted on dense Hermitian matrices from real applications as well as large sparse matrices from the SuiteSparse and ELSES collections.This work was supported in part by National Key R&D Program of China under Grant 2023YFB3001700, in part by National NaturalScience Foundation of China under Grant U1611261, Grant 61872392, andGrant U1811461. The work of J. E. Roman was supported in part by MICIU/AEI/10.13039/501100011033 under Grant PID2022-139568NB-I00, andin part by ERDF/EU under Grant RED2022-134176-T.Institute of Electrical and Electronics EngineersDepartamento de Sistemas Informáticos y ComputaciónEscuela Técnica Superior de Ingeniería InformáticaAGENCIA ESTATAL DE INVESTIGACIONAgencia Estatal de InvestigaciónEuropean Regional Development FundNational Natural Science Foundation of ChinaNational Key Research and Development Program of ChinaRepositorio Institucional de la Universitat Politècnica de València Riunet20262026-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/231178reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 PID2022-139568NB-I00 ALGORITMOS PARALELOS Y SOFTWARE PARA CALCULO ESPECTRAL EN APLICACIONES DE FISICA COMPUTACIONALNational Natural Science Foundation of China https://doi.org/10.13039/501100001809 U1611261National Natural Science Foundation of China https://doi.org/10.13039/501100001809 61872392National Natural Science Foundation of China https://doi.org/10.13039/501100001809 U1811461National Key Research and Development Program of China https://doi.org/10.13039/501100012166 2023YFB3001700Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 RED2022-134176-Topen accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2311782026-06-13T07:49:27Z
dc.title.none.fl_str_mv PHIDE: A Parallel Hybrid Direct-Iterative Eigensolver for Hermitian Eigenvalue Problems
title PHIDE: A Parallel Hybrid Direct-Iterative Eigensolver for Hermitian Eigenvalue Problems
spellingShingle PHIDE: A Parallel Hybrid Direct-Iterative Eigensolver for Hermitian Eigenvalue Problems
Li, Shengguo
Eigenvalues
Spectrum-slicing algorithms
Banded matrices
Direct eigenvalue methods
title_short PHIDE: A Parallel Hybrid Direct-Iterative Eigensolver for Hermitian Eigenvalue Problems
title_full PHIDE: A Parallel Hybrid Direct-Iterative Eigensolver for Hermitian Eigenvalue Problems
title_fullStr PHIDE: A Parallel Hybrid Direct-Iterative Eigensolver for Hermitian Eigenvalue Problems
title_full_unstemmed PHIDE: A Parallel Hybrid Direct-Iterative Eigensolver for Hermitian Eigenvalue Problems
title_sort PHIDE: A Parallel Hybrid Direct-Iterative Eigensolver for Hermitian Eigenvalue Problems
dc.creator.none.fl_str_mv Li, Shengguo
Wu, Xinzhe
Yuan, Ziyang
Wang, Ruibo
Li, Tiejun
Xie, Yi
Yang, Bo
Chen, Xuguang
Jose E. Roman|||0000-0003-1144-6772
author Li, Shengguo
author_facet Li, Shengguo
Wu, Xinzhe
Yuan, Ziyang
Wang, Ruibo
Li, Tiejun
Xie, Yi
Yang, Bo
Chen, Xuguang
Jose E. Roman|||0000-0003-1144-6772
author_role author
author2 Wu, Xinzhe
Yuan, Ziyang
Wang, Ruibo
Li, Tiejun
Xie, Yi
Yang, Bo
Chen, Xuguang
Jose E. Roman|||0000-0003-1144-6772
author2_role author
author
author
author
author
author
author
author
dc.contributor.none.fl_str_mv Departamento de Sistemas Informáticos y Computación
Escuela Técnica Superior de Ingeniería Informática
AGENCIA ESTATAL DE INVESTIGACION
Agencia Estatal de Investigación
European Regional Development Fund
National Natural Science Foundation of China
National Key Research and Development Program of China
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Eigenvalues
Spectrum-slicing algorithms
Banded matrices
Direct eigenvalue methods
topic Eigenvalues
Spectrum-slicing algorithms
Banded matrices
Direct eigenvalue methods
description [EN] In this paper, we propose a Parallel Hybrid Direct-Iterative Eigensolver for Hermitian Eigenvalue Problems without tridiagonalization, denoted by PHIDE, which combines direct and iterative methods. PHIDE first reduces a Hermitian matrix to banded form, then applies a spectrum slicing algorithm to the banded matrix, and finally computes the eigenvectors of the original matrix via backtransformation. Compared with conventional direct eigensolvers, PHIDE avoids tridiagonalization, which involves many memory-bound operations. In PHIDE, the banded eigenvalue problem is solved using the contour integral method implemented in FEAST, which may yield slightly lower accuracy than tridiagonalization-based approaches. For sequences of correlated Hermitian eigenvalue problems arising in density functional theory (DFT), PHIDE achieves an average speedup of 1.22x over the state-of-the-art direct solver in ELPA when using 1024 processes. Numerical experiments are conducted on dense Hermitian matrices from real applications as well as large sparse matrices from the SuiteSparse and ELSES collections.
publishDate 2026
dc.date.none.fl_str_mv 2026
2026-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/231178
url https://riunet.upv.es/handle/10251/231178
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 PID2022-139568NB-I00 ALGORITMOS PARALELOS Y SOFTWARE PARA CALCULO ESPECTRAL EN APLICACIONES DE FISICA COMPUTACIONAL
National Natural Science Foundation of China https://doi.org/10.13039/501100001809 U1611261
National Natural Science Foundation of China https://doi.org/10.13039/501100001809 61872392
National Natural Science Foundation of China https://doi.org/10.13039/501100001809 U1811461
National Key Research and Development Program of China https://doi.org/10.13039/501100012166 2023YFB3001700
Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 RED2022-134176-T
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers
publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.812429

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