The effect of the nonlinearity on GCV applied to conjugate gradients in computerized tomography

Detalhes bibliográficos
Autor(a) principal: Santos,Reginaldo J.
Data de Publicação: 2006
Outros Autores: Pierro,Álvaro R. de
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Computational & Applied Mathematics
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022006000100006
Resumo: We study the effect of the nonlinear dependence of the iterate x k of Conjugate Gradients method (CG) from the data b in the GCV procedure to stop the iterations. We compare two versions of using GCV to stop CG. In one version we compute the GCV function with the iterate x k depending linearly from the data b and the other one depending nonlinearly. We have tested the two versions in a large scale problem: positron emission tomography (PET). Our results suggest the necessity of considering the nonlinearity for the GCV function to obtain a reasonable stopping criterion.
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spelling The effect of the nonlinearity on GCV applied to conjugate gradients in computerized tomographyGeneralized Cross ValidationTomographyConjugate GradientsWe study the effect of the nonlinear dependence of the iterate x k of Conjugate Gradients method (CG) from the data b in the GCV procedure to stop the iterations. We compare two versions of using GCV to stop CG. In one version we compute the GCV function with the iterate x k depending linearly from the data b and the other one depending nonlinearly. We have tested the two versions in a large scale problem: positron emission tomography (PET). Our results suggest the necessity of considering the nonlinearity for the GCV function to obtain a reasonable stopping criterion.Sociedade Brasileira de Matemática Aplicada e Computacional2006-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022006000100006Computational & Applied Mathematics v.25 n.1 2006reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMACinfo:eu-repo/semantics/openAccessSantos,Reginaldo J.Pierro,Álvaro R. deeng2006-09-27T00:00:00Zoai:scielo:S1807-03022006000100006Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2006-09-27T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false
dc.title.none.fl_str_mv The effect of the nonlinearity on GCV applied to conjugate gradients in computerized tomography
title The effect of the nonlinearity on GCV applied to conjugate gradients in computerized tomography
spellingShingle The effect of the nonlinearity on GCV applied to conjugate gradients in computerized tomography
Santos,Reginaldo J.
Generalized Cross Validation
Tomography
Conjugate Gradients
title_short The effect of the nonlinearity on GCV applied to conjugate gradients in computerized tomography
title_full The effect of the nonlinearity on GCV applied to conjugate gradients in computerized tomography
title_fullStr The effect of the nonlinearity on GCV applied to conjugate gradients in computerized tomography
title_full_unstemmed The effect of the nonlinearity on GCV applied to conjugate gradients in computerized tomography
title_sort The effect of the nonlinearity on GCV applied to conjugate gradients in computerized tomography
author Santos,Reginaldo J.
author_facet Santos,Reginaldo J.
Pierro,Álvaro R. de
author_role author
author2 Pierro,Álvaro R. de
author2_role author
dc.contributor.author.fl_str_mv Santos,Reginaldo J.
Pierro,Álvaro R. de
dc.subject.por.fl_str_mv Generalized Cross Validation
Tomography
Conjugate Gradients
topic Generalized Cross Validation
Tomography
Conjugate Gradients
description We study the effect of the nonlinear dependence of the iterate x k of Conjugate Gradients method (CG) from the data b in the GCV procedure to stop the iterations. We compare two versions of using GCV to stop CG. In one version we compute the GCV function with the iterate x k depending linearly from the data b and the other one depending nonlinearly. We have tested the two versions in a large scale problem: positron emission tomography (PET). Our results suggest the necessity of considering the nonlinearity for the GCV function to obtain a reasonable stopping criterion.
publishDate 2006
dc.date.none.fl_str_mv 2006-01-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022006000100006
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022006000100006
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv Computational & Applied Mathematics v.25 n.1 2006
reponame:Computational & Applied Mathematics
instname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
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instname_str Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
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reponame_str Computational & Applied Mathematics
collection Computational & Applied Mathematics
repository.name.fl_str_mv Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
repository.mail.fl_str_mv ||sbmac@sbmac.org.br
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