Improving the accuracy of the adaptive cross approximation with a convergence criterion based on random sampling

The accuracy of the Adaptive Cross Approximation (ACA) algorithm, a popular method for the compression of low rank matrix blocks in Method of Moment computations, is sometimes seriously compromised by unpredictable errors in the convergence criterion. This paper proposes an alternative criterion, ba...

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Autores: Heldring, Alexander|||0000-0003-2011-2096, Úbeda Farré, Eduard|||0000-0001-6759-0445, Rius Casals, Juan Manuel|||0000-0003-0606-5422
Formato: artículo
Fecha de publicación:2020
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/337061
Acesso em linha:https://hdl.handle.net/2117/337061
https://dx.doi.org/10.1109/TAP.2020.3010857
Access Level:acceso abierto
Palavra-chave:Computer algorithms
Signal processing
Adaptive cross approximation (ACA)
Computational electromagnetics
Fast solvers
Method of moments
Algorismes computacionals
Tractament del senyal
Àrees temàtiques de la UPC::Enginyeria de la telecomunicació::Processament del senyal
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oai_identifier_str oai:upcommons.upc.edu:2117/337061
network_acronym_str ES
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repository_id_str
spelling Improving the accuracy of the adaptive cross approximation with a convergence criterion based on random samplingHeldring, Alexander|||0000-0003-2011-2096Úbeda Farré, Eduard|||0000-0001-6759-0445Rius Casals, Juan Manuel|||0000-0003-0606-5422Computer algorithmsSignal processingAdaptive cross approximation (ACA)Computational electromagneticsFast solversMethod of momentsAlgorismes computacionalsTractament del senyalÀrees temàtiques de la UPC::Enginyeria de la telecomunicació::Processament del senyalThe accuracy of the Adaptive Cross Approximation (ACA) algorithm, a popular method for the compression of low rank matrix blocks in Method of Moment computations, is sometimes seriously compromised by unpredictable errors in the convergence criterion. This paper proposes an alternative criterion, based on global sampling of the error in the elements of the ACA compressed matrix. The sampling error depends on the size of the sample but also on the population distribution of the error, which makes it difficult to control the error independently of the underlying problem. However, as argued and demonstrated in the paper, the distribution of the error converges to the same unique probability distribution function for all low rank matrices. Complementing the sampling criterion with a simple mechanism to detect this convergence, we arrive at a criterion that controls the error irrespective of the underlying problem. As a practical example the RCS of a moderate size metallic ogive is computed to illustrate the merits of the proposed criterion. The proposed algorithm may also be useful in other methods that approximate low-rank matrices by interpolation of a reduced set of its elements.This work was partly funded by the Ministerio de Ciencia e Innovacion (MICINN) under projects TEC2016-78028-C3-1-P, TEC2017-84817-C2-2-R, TEC2017-83343-C4-2-R, PID 2019-107885GBC31, MDM2016-0600, and Catalan Research Group 2017 SGR 219.Peer Reviewed20202020-07-2720212021-02-08journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/337061https://dx.doi.org/10.1109/TAP.2020.3010857reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengAgencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 TEC2017-84817-C2-2-R SENSORES GRAVIMETRICOS DE GASES BASADOS EN RESONADORES ELECTRO-ACUSTICOS DE ALN PARA APLICACIONES EN TEMPERATURAS EXTREMASAgencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 TEC2017-83343-C4-2-R SOLUCIONES AVANZADAS DE PROCESADO DIGITAL DE SEÑAL PARA COMPONENTES Y SISTEMAS DE NUEVA RADIO 5G ENERGETICA Y COMPUTACIONALMENTE EFICIENTESAgencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2019-107885GB-C31 SISTEMAS RADIANTES X-WAVE INTEGRADAS DE COMUNICACIONES Y SENSORIZACIONopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3370612026-05-27T15:37:01Z
dc.title.none.fl_str_mv Improving the accuracy of the adaptive cross approximation with a convergence criterion based on random sampling
title Improving the accuracy of the adaptive cross approximation with a convergence criterion based on random sampling
spellingShingle Improving the accuracy of the adaptive cross approximation with a convergence criterion based on random sampling
Heldring, Alexander|||0000-0003-2011-2096
Computer algorithms
Signal processing
Adaptive cross approximation (ACA)
Computational electromagnetics
Fast solvers
Method of moments
Algorismes computacionals
Tractament del senyal
Àrees temàtiques de la UPC::Enginyeria de la telecomunicació::Processament del senyal
title_short Improving the accuracy of the adaptive cross approximation with a convergence criterion based on random sampling
title_full Improving the accuracy of the adaptive cross approximation with a convergence criterion based on random sampling
title_fullStr Improving the accuracy of the adaptive cross approximation with a convergence criterion based on random sampling
title_full_unstemmed Improving the accuracy of the adaptive cross approximation with a convergence criterion based on random sampling
title_sort Improving the accuracy of the adaptive cross approximation with a convergence criterion based on random sampling
dc.creator.none.fl_str_mv Heldring, Alexander|||0000-0003-2011-2096
Úbeda Farré, Eduard|||0000-0001-6759-0445
Rius Casals, Juan Manuel|||0000-0003-0606-5422
author Heldring, Alexander|||0000-0003-2011-2096
author_facet Heldring, Alexander|||0000-0003-2011-2096
Úbeda Farré, Eduard|||0000-0001-6759-0445
Rius Casals, Juan Manuel|||0000-0003-0606-5422
author_role author
author2 Úbeda Farré, Eduard|||0000-0001-6759-0445
Rius Casals, Juan Manuel|||0000-0003-0606-5422
author2_role author
author
dc.subject.none.fl_str_mv Computer algorithms
Signal processing
Adaptive cross approximation (ACA)
Computational electromagnetics
Fast solvers
Method of moments
Algorismes computacionals
Tractament del senyal
Àrees temàtiques de la UPC::Enginyeria de la telecomunicació::Processament del senyal
topic Computer algorithms
Signal processing
Adaptive cross approximation (ACA)
Computational electromagnetics
Fast solvers
Method of moments
Algorismes computacionals
Tractament del senyal
Àrees temàtiques de la UPC::Enginyeria de la telecomunicació::Processament del senyal
description The accuracy of the Adaptive Cross Approximation (ACA) algorithm, a popular method for the compression of low rank matrix blocks in Method of Moment computations, is sometimes seriously compromised by unpredictable errors in the convergence criterion. This paper proposes an alternative criterion, based on global sampling of the error in the elements of the ACA compressed matrix. The sampling error depends on the size of the sample but also on the population distribution of the error, which makes it difficult to control the error independently of the underlying problem. However, as argued and demonstrated in the paper, the distribution of the error converges to the same unique probability distribution function for all low rank matrices. Complementing the sampling criterion with a simple mechanism to detect this convergence, we arrive at a criterion that controls the error irrespective of the underlying problem. As a practical example the RCS of a moderate size metallic ogive is computed to illustrate the merits of the proposed criterion. The proposed algorithm may also be useful in other methods that approximate low-rank matrices by interpolation of a reduced set of its elements.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-07-27
2021
2021-02-08
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/337061
https://dx.doi.org/10.1109/TAP.2020.3010857
url https://hdl.handle.net/2117/337061
https://dx.doi.org/10.1109/TAP.2020.3010857
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://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 TEC2017-84817-C2-2-R SENSORES GRAVIMETRICOS DE GASES BASADOS EN RESONADORES ELECTRO-ACUSTICOS DE ALN PARA APLICACIONES EN TEMPERATURAS EXTREMAS
Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 TEC2017-83343-C4-2-R SOLUCIONES AVANZADAS DE PROCESADO DIGITAL DE SEÑAL PARA COMPONENTES Y SISTEMAS DE NUEVA RADIO 5G ENERGETICA Y COMPUTACIONALMENTE EFICIENTES
Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2019-107885GB-C31 SISTEMAS RADIANTES X-WAVE INTEGRADAS DE COMUNICACIONES Y SENSORIZACION
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
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
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300719

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