The nearest generalized doubly stochastic matrix to a real matrix with the same firstand second moments

Detalhes bibliográficos
Autor(a) principal: Glunt,William
Data de Publicação: 2008
Outros Autores: Hayden,Thomas L., Reams,Robert
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Computational & Applied Mathematics
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022008000200005
Resumo: Let T be an arbitrary n × n matrix with real entries. We explicitly find the closest (in Frobenius norm) matrix A to T, where A is n × n with real entries, subject to the condition that A is ''generalized doubly stochastic'' (i.e. Ae = e and eT A = eT, where e = (1,1,...,1)T, although A is not necessarily nonnegative) and A has the same first moment as T (i.e. e1T Ae1 = e1T Te1). We also explicitly find the closest matrix A to T when A is generalized doubly stochastic has the same first moment as T and the same second moment as T (i.e. e1T A²e1 = e1T T²e1), when such a matrix A exists.
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spelling The nearest generalized doubly stochastic matrix to a real matrix with the same firstand second momentsdoubly stochasticgeneralized doubly stochasticmomentsnearest matrixclosest matrixFrobenius normLet T be an arbitrary n × n matrix with real entries. We explicitly find the closest (in Frobenius norm) matrix A to T, where A is n × n with real entries, subject to the condition that A is ''generalized doubly stochastic'' (i.e. Ae = e and eT A = eT, where e = (1,1,...,1)T, although A is not necessarily nonnegative) and A has the same first moment as T (i.e. e1T Ae1 = e1T Te1). We also explicitly find the closest matrix A to T when A is generalized doubly stochastic has the same first moment as T and the same second moment as T (i.e. e1T A²e1 = e1T T²e1), when such a matrix A exists.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=S1807-03022008000200005Computational & Applied Mathematics v.27 n.2 2008reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S0101-82052008000200005info:eu-repo/semantics/openAccessGlunt,WilliamHayden,Thomas L.Reams,Roberteng2008-07-21T00:00:00Zoai:scielo:S1807-03022008000200005Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2008-07-21T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false
dc.title.none.fl_str_mv The nearest generalized doubly stochastic matrix to a real matrix with the same firstand second moments
title The nearest generalized doubly stochastic matrix to a real matrix with the same firstand second moments
spellingShingle The nearest generalized doubly stochastic matrix to a real matrix with the same firstand second moments
Glunt,William
doubly stochastic
generalized doubly stochastic
moments
nearest matrix
closest matrix
Frobenius norm
title_short The nearest generalized doubly stochastic matrix to a real matrix with the same firstand second moments
title_full The nearest generalized doubly stochastic matrix to a real matrix with the same firstand second moments
title_fullStr The nearest generalized doubly stochastic matrix to a real matrix with the same firstand second moments
title_full_unstemmed The nearest generalized doubly stochastic matrix to a real matrix with the same firstand second moments
title_sort The nearest generalized doubly stochastic matrix to a real matrix with the same firstand second moments
author Glunt,William
author_facet Glunt,William
Hayden,Thomas L.
Reams,Robert
author_role author
author2 Hayden,Thomas L.
Reams,Robert
author2_role author
author
dc.contributor.author.fl_str_mv Glunt,William
Hayden,Thomas L.
Reams,Robert
dc.subject.por.fl_str_mv doubly stochastic
generalized doubly stochastic
moments
nearest matrix
closest matrix
Frobenius norm
topic doubly stochastic
generalized doubly stochastic
moments
nearest matrix
closest matrix
Frobenius norm
description Let T be an arbitrary n × n matrix with real entries. We explicitly find the closest (in Frobenius norm) matrix A to T, where A is n × n with real entries, subject to the condition that A is ''generalized doubly stochastic'' (i.e. Ae = e and eT A = eT, where e = (1,1,...,1)T, although A is not necessarily nonnegative) and A has the same first moment as T (i.e. e1T Ae1 = e1T Te1). We also explicitly find the closest matrix A to T when A is generalized doubly stochastic has the same first moment as T and the same second moment as T (i.e. e1T A²e1 = e1T T²e1), when such a matrix A exists.
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=S1807-03022008000200005
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022008000200005
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0101-82052008000200005
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.2 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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