Generalizations of Aitken's process for accelerating the convergence of sequences

Detalhes bibliográficos
Autor(a) principal: Brezinski,Claude
Data de Publicação: 2007
Outros Autores: Redivo Zaglia,Michela
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Computational & Applied Mathematics
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022007000200001
Resumo: When a sequence or an iterative process is slowly converging, a convergence acceleration process has to be used. It consists in transforming the slowly converging sequence into a new one which, under some assumptions, converges faster to the same limit. In this paper, new scalar sequence transformations having a kernel (the set of sequences transformed into a constant sequence) generalizing the kernel of the Aitken's delta2 process are constructed. Then, these transformations are extended to vector sequences. They also lead to new fixed point methods which are studied.
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spelling Generalizations of Aitken's process for accelerating the convergence of sequencesconvergence accelerationAitken processextrapolationfixed point methodsWhen a sequence or an iterative process is slowly converging, a convergence acceleration process has to be used. It consists in transforming the slowly converging sequence into a new one which, under some assumptions, converges faster to the same limit. In this paper, new scalar sequence transformations having a kernel (the set of sequences transformed into a constant sequence) generalizing the kernel of the Aitken's delta2 process are constructed. Then, these transformations are extended to vector sequences. They also lead to new fixed point methods which are studied.Sociedade Brasileira de Matemática Aplicada e Computacional2007-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022007000200001Computational & Applied Mathematics v.26 n.2 2007reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S0101-82052007000200001info:eu-repo/semantics/openAccessBrezinski,ClaudeRedivo Zaglia,Michelaeng2008-01-09T00:00:00Zoai:scielo:S1807-03022007000200001Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2008-01-09T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false
dc.title.none.fl_str_mv Generalizations of Aitken's process for accelerating the convergence of sequences
title Generalizations of Aitken's process for accelerating the convergence of sequences
spellingShingle Generalizations of Aitken's process for accelerating the convergence of sequences
Brezinski,Claude
convergence acceleration
Aitken process
extrapolation
fixed point methods
title_short Generalizations of Aitken's process for accelerating the convergence of sequences
title_full Generalizations of Aitken's process for accelerating the convergence of sequences
title_fullStr Generalizations of Aitken's process for accelerating the convergence of sequences
title_full_unstemmed Generalizations of Aitken's process for accelerating the convergence of sequences
title_sort Generalizations of Aitken's process for accelerating the convergence of sequences
author Brezinski,Claude
author_facet Brezinski,Claude
Redivo Zaglia,Michela
author_role author
author2 Redivo Zaglia,Michela
author2_role author
dc.contributor.author.fl_str_mv Brezinski,Claude
Redivo Zaglia,Michela
dc.subject.por.fl_str_mv convergence acceleration
Aitken process
extrapolation
fixed point methods
topic convergence acceleration
Aitken process
extrapolation
fixed point methods
description When a sequence or an iterative process is slowly converging, a convergence acceleration process has to be used. It consists in transforming the slowly converging sequence into a new one which, under some assumptions, converges faster to the same limit. In this paper, new scalar sequence transformations having a kernel (the set of sequences transformed into a constant sequence) generalizing the kernel of the Aitken's delta2 process are constructed. Then, these transformations are extended to vector sequences. They also lead to new fixed point methods which are studied.
publishDate 2007
dc.date.none.fl_str_mv 2007-01-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022007000200001
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022007000200001
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0101-82052007000200001
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.26 n.2 2007
reponame:Computational & Applied Mathematics
instname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron_str SBMAC
institution SBMAC
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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