Parallel Arnoldi eigensolvers with enhanced scalability via global communications rearrangement

[EN] This paper presents several new variants of the single-vector Arnoldi algorithm for computing approximations to eigenvalues and eigenvectors of a non-symmetric matrix. The context of this work is the efficient implementation of industrial-strength, parallel, sparse eigensolvers, in which robust...

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Authors: Hernandez, V., Jose E. Roman|||0000-0003-1144-6772, Tomás Domínguez, Andrés Enrique
Format: article
Publication Date:2007
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/232925
Online Access:https://riunet.upv.es/handle/10251/232925
Access Level:Open access
Keyword:Arnoldi eigensolvers
Iterative Gram-Schmidt orthogonalization
Distributed-memory programming
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spelling Parallel Arnoldi eigensolvers with enhanced scalability via global communications rearrangementHernandez, V.Jose E. Roman|||0000-0003-1144-6772Tomás Domínguez, Andrés EnriqueArnoldi eigensolversIterative Gram-Schmidt orthogonalizationDistributed-memory programming[EN] This paper presents several new variants of the single-vector Arnoldi algorithm for computing approximations to eigenvalues and eigenvectors of a non-symmetric matrix. The context of this work is the efficient implementation of industrial-strength, parallel, sparse eigensolvers, in which robustness is of paramount importance, as well as efficiency. For this reason, Arnoldi variants that employ Gram-Schmidt with iterative reorthogonalization are considered. The proposed algorithms aim at improving the scalability when running in massively parallel platforms with many processors. The main goal is to reduce the performance penalty induced by global communications required in vector inner products and norms. In the proposed algorithms, this is achieved by reorganizing the stages that involve these operations, particularly the orthogonalization and normalization of vectors, in such a way that several global communications are grouped together while Guaranteeing that the numerical stability of the process is maintained. The numerical properties of the new algorithms are assessed by means of a large set of test matrices. Also, scalability analyses show a significant improvement in parallel performance.This work was supported in part by the Valencian Regional Administration, Directorate of Research and Technology Transfer, under grant number GV06/091. Part of this research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the US Department of Energy under Contract No. DE-AC03- 76SF00098. The authors thankfully acknowledge the computer resources, technical expertise and assistance provided by the Barcelona Supercomputing Center Centro Nacional de Supercomputacio¿n.ElsevierDepartamento de Informática de Sistemas y ComputadoresDepartamento de Sistemas Informáticos y ComputaciónEscuela Técnica Superior de Ingeniería InformáticaGeneralitat ValencianaU.S. Department of EnergyRepositorio Institucional de la Universitat Politècnica de València Riunet20072007-08-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/232925reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengU.S. Department of Energy https://doi.org/10.13039/100000015 DE-AC03-76SF00098 Advanced Instrumentations for Microscopies of Molecular MachinesGeneralitat Valenciana https://doi.org/10.13039/501100003359 GV06%2F091open accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2329252026-06-13T07:49:27Z
dc.title.none.fl_str_mv Parallel Arnoldi eigensolvers with enhanced scalability via global communications rearrangement
title Parallel Arnoldi eigensolvers with enhanced scalability via global communications rearrangement
spellingShingle Parallel Arnoldi eigensolvers with enhanced scalability via global communications rearrangement
Hernandez, V.
Arnoldi eigensolvers
Iterative Gram-Schmidt orthogonalization
Distributed-memory programming
title_short Parallel Arnoldi eigensolvers with enhanced scalability via global communications rearrangement
title_full Parallel Arnoldi eigensolvers with enhanced scalability via global communications rearrangement
title_fullStr Parallel Arnoldi eigensolvers with enhanced scalability via global communications rearrangement
title_full_unstemmed Parallel Arnoldi eigensolvers with enhanced scalability via global communications rearrangement
title_sort Parallel Arnoldi eigensolvers with enhanced scalability via global communications rearrangement
dc.creator.none.fl_str_mv Hernandez, V.
Jose E. Roman|||0000-0003-1144-6772
Tomás Domínguez, Andrés Enrique
author Hernandez, V.
author_facet Hernandez, V.
Jose E. Roman|||0000-0003-1144-6772
Tomás Domínguez, Andrés Enrique
author_role author
author2 Jose E. Roman|||0000-0003-1144-6772
Tomás Domínguez, Andrés Enrique
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Informática de Sistemas y Computadores
Departamento de Sistemas Informáticos y Computación
Escuela Técnica Superior de Ingeniería Informática
Generalitat Valenciana
U.S. Department of Energy
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Arnoldi eigensolvers
Iterative Gram-Schmidt orthogonalization
Distributed-memory programming
topic Arnoldi eigensolvers
Iterative Gram-Schmidt orthogonalization
Distributed-memory programming
description [EN] This paper presents several new variants of the single-vector Arnoldi algorithm for computing approximations to eigenvalues and eigenvectors of a non-symmetric matrix. The context of this work is the efficient implementation of industrial-strength, parallel, sparse eigensolvers, in which robustness is of paramount importance, as well as efficiency. For this reason, Arnoldi variants that employ Gram-Schmidt with iterative reorthogonalization are considered. The proposed algorithms aim at improving the scalability when running in massively parallel platforms with many processors. The main goal is to reduce the performance penalty induced by global communications required in vector inner products and norms. In the proposed algorithms, this is achieved by reorganizing the stages that involve these operations, particularly the orthogonalization and normalization of vectors, in such a way that several global communications are grouped together while Guaranteeing that the numerical stability of the process is maintained. The numerical properties of the new algorithms are assessed by means of a large set of test matrices. Also, scalability analyses show a significant improvement in parallel performance.
publishDate 2007
dc.date.none.fl_str_mv 2007
2007-08-01
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/10251/232925
url https://riunet.upv.es/handle/10251/232925
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv U.S. Department of Energy https://doi.org/10.13039/100000015 DE-AC03-76SF00098 Advanced Instrumentations for Microscopies of Molecular Machines
Generalitat Valenciana https://doi.org/10.13039/501100003359 GV06%2F091
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
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
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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 15.198674

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