An efficient Newton-type method with fifth-order convergence for solving nonlinear equations

Detalhes bibliográficos
Autor(a) principal: Fang,Liang
Data de Publicação: 2008
Outros Autores: Sun,Li, He,Guoping
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Computational & Applied Mathematics
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022008000300003
Resumo: In this paper, we present an efficient Newton-like method with fifth-order convergence for nonlinear equations. The algorithm is free from second derivative and it requires four evaluations of the given function and its first derivative at each iteration. As a consequence, its efficiency index is equal to 4√5 which is better than that of Newton's method √2. Several examples demonstrate that the presented algorithm is more efficient and performs better than Newton's method.
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spelling An efficient Newton-type method with fifth-order convergence for solving nonlinear equationsNewton's methoditerative methodnonlinear equationsorder of convergenceIn this paper, we present an efficient Newton-like method with fifth-order convergence for nonlinear equations. The algorithm is free from second derivative and it requires four evaluations of the given function and its first derivative at each iteration. As a consequence, its efficiency index is equal to 4√5 which is better than that of Newton's method √2. Several examples demonstrate that the presented algorithm is more efficient and performs better than Newton's method.Sociedade Brasileira de Matemática Aplicada e Computacional2008-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022008000300003Computational & Applied Mathematics v.27 n.3 2008reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMACinfo:eu-repo/semantics/openAccessFang,LiangSun,LiHe,Guopingeng2008-10-29T00:00:00Zoai:scielo:S1807-03022008000300003Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2008-10-29T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false
dc.title.none.fl_str_mv An efficient Newton-type method with fifth-order convergence for solving nonlinear equations
title An efficient Newton-type method with fifth-order convergence for solving nonlinear equations
spellingShingle An efficient Newton-type method with fifth-order convergence for solving nonlinear equations
Fang,Liang
Newton's method
iterative method
nonlinear equations
order of convergence
title_short An efficient Newton-type method with fifth-order convergence for solving nonlinear equations
title_full An efficient Newton-type method with fifth-order convergence for solving nonlinear equations
title_fullStr An efficient Newton-type method with fifth-order convergence for solving nonlinear equations
title_full_unstemmed An efficient Newton-type method with fifth-order convergence for solving nonlinear equations
title_sort An efficient Newton-type method with fifth-order convergence for solving nonlinear equations
author Fang,Liang
author_facet Fang,Liang
Sun,Li
He,Guoping
author_role author
author2 Sun,Li
He,Guoping
author2_role author
author
dc.contributor.author.fl_str_mv Fang,Liang
Sun,Li
He,Guoping
dc.subject.por.fl_str_mv Newton's method
iterative method
nonlinear equations
order of convergence
topic Newton's method
iterative method
nonlinear equations
order of convergence
description In this paper, we present an efficient Newton-like method with fifth-order convergence for nonlinear equations. The algorithm is free from second derivative and it requires four evaluations of the given function and its first derivative at each iteration. As a consequence, its efficiency index is equal to 4√5 which is better than that of Newton's method √2. Several examples demonstrate that the presented algorithm is more efficient and performs better than Newton's method.
publishDate 2008
dc.date.none.fl_str_mv 2008-01-01
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=S1807-03022008000300003
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022008000300003
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.27 n.3 2008
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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