Linear Algebra and Differential Calculus in Pseudo-Intervals Vector Space

Detalhes bibliográficos
Autor(a) principal: KENOUFI,A.
Data de Publicação: 2016
Tipo de documento: Artigo
Idioma: eng
Título da fonte: TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512016000300283
Resumo: ABSTRACT. In this paper one proposes to use a new approach of interval arithmetic, the so-called pseudo-intervals (1), (5), (13). It uses a construction which is more canonical and based on the semi-group completion into the group, and it allows to build a Banach vector space. This is achieved by embedding the vector space into free algebra of dimensions higher than 4. It permits to perform linear algebra and differential calculus with pseudo-intervals. Some numerical applications for interval matrix eigenmode calculation, inversion and function minimization are exhibited for simple examples.
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spelling Linear Algebra and Differential Calculus in Pseudo-Intervals Vector SpacePseudo-intervals arithmeticfree algebrainclusion functionlinear algebradifferential calculusoptimizationABSTRACT. In this paper one proposes to use a new approach of interval arithmetic, the so-called pseudo-intervals (1), (5), (13). It uses a construction which is more canonical and based on the semi-group completion into the group, and it allows to build a Banach vector space. This is achieved by embedding the vector space into free algebra of dimensions higher than 4. It permits to perform linear algebra and differential calculus with pseudo-intervals. Some numerical applications for interval matrix eigenmode calculation, inversion and function minimization are exhibited for simple examples.Sociedade Brasileira de Matemática Aplicada e Computacional2016-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512016000300283TEMA (São Carlos) v.17 n.3 2016reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)instname:Sociedade Brasileira de Matemática Aplicada e Computacionalinstacron:SBMAC10.5540/tema.2016.017.03.0283info:eu-repo/semantics/openAccessKENOUFI,A.eng2017-01-05T00:00:00Zoai:scielo:S2179-84512016000300283Revistahttp://www.scielo.br/temaPUBhttps://old.scielo.br/oai/scielo-oai.phpcastelo@icmc.usp.br2179-84511677-1966opendoar:2017-01-05T00:00TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacionalfalse
dc.title.none.fl_str_mv Linear Algebra and Differential Calculus in Pseudo-Intervals Vector Space
title Linear Algebra and Differential Calculus in Pseudo-Intervals Vector Space
spellingShingle Linear Algebra and Differential Calculus in Pseudo-Intervals Vector Space
KENOUFI,A.
Pseudo-intervals arithmetic
free algebra
inclusion function
linear algebra
differential calculus
optimization
title_short Linear Algebra and Differential Calculus in Pseudo-Intervals Vector Space
title_full Linear Algebra and Differential Calculus in Pseudo-Intervals Vector Space
title_fullStr Linear Algebra and Differential Calculus in Pseudo-Intervals Vector Space
title_full_unstemmed Linear Algebra and Differential Calculus in Pseudo-Intervals Vector Space
title_sort Linear Algebra and Differential Calculus in Pseudo-Intervals Vector Space
author KENOUFI,A.
author_facet KENOUFI,A.
author_role author
dc.contributor.author.fl_str_mv KENOUFI,A.
dc.subject.por.fl_str_mv Pseudo-intervals arithmetic
free algebra
inclusion function
linear algebra
differential calculus
optimization
topic Pseudo-intervals arithmetic
free algebra
inclusion function
linear algebra
differential calculus
optimization
description ABSTRACT. In this paper one proposes to use a new approach of interval arithmetic, the so-called pseudo-intervals (1), (5), (13). It uses a construction which is more canonical and based on the semi-group completion into the group, and it allows to build a Banach vector space. This is achieved by embedding the vector space into free algebra of dimensions higher than 4. It permits to perform linear algebra and differential calculus with pseudo-intervals. Some numerical applications for interval matrix eigenmode calculation, inversion and function minimization are exhibited for simple examples.
publishDate 2016
dc.date.none.fl_str_mv 2016-12-01
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=S2179-84512016000300283
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512016000300283
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.5540/tema.2016.017.03.0283
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 TEMA (São Carlos) v.17 n.3 2016
reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
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instacron_str SBMAC
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reponame_str TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
collection TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
repository.name.fl_str_mv TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacional
repository.mail.fl_str_mv castelo@icmc.usp.br
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