Matrix differential equations and inverse preconditioners
Autor(a) principal: | |
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Data de Publicação: | 2007 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Computational & Applied Mathematics |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022007000100005 |
Resumo: | In this article, we propose to model the inverse of a given matrix as the state of a proper first order matrix differential equation. The inverse can correspond to a finite value of the independent variable or can be reached as a steady state. In both cases we derive corresponding dynamical systems and establish stability and convergence results. The application of a numerical time marching scheme is then proposed to compute an approximation of the inverse. The study of the underlying schemes can be done by using tools of numerical analysis instead of linear algebra techniques only. With our approach, we recover some known schemes but also introduce new ones. We derive in addition a masked dynamical system for computing sparse inverse approximations. Finally we give numerical results that illustrate the validity of our approach. |
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Computational & Applied Mathematics |
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Matrix differential equations and inverse preconditionersmatrix differential equationnumerical schemesnumerical linear algebrapreconditioningIn this article, we propose to model the inverse of a given matrix as the state of a proper first order matrix differential equation. The inverse can correspond to a finite value of the independent variable or can be reached as a steady state. In both cases we derive corresponding dynamical systems and establish stability and convergence results. The application of a numerical time marching scheme is then proposed to compute an approximation of the inverse. The study of the underlying schemes can be done by using tools of numerical analysis instead of linear algebra techniques only. With our approach, we recover some known schemes but also introduce new ones. We derive in addition a masked dynamical system for computing sparse inverse approximations. Finally we give numerical results that illustrate the validity of our approach.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=S1807-03022007000100005Computational & Applied Mathematics v.26 n.1 2007reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMACinfo:eu-repo/semantics/openAccessChehab,Jean-Pauleng2007-05-10T00:00:00Zoai:scielo:S1807-03022007000100005Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2007-05-10T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false |
dc.title.none.fl_str_mv |
Matrix differential equations and inverse preconditioners |
title |
Matrix differential equations and inverse preconditioners |
spellingShingle |
Matrix differential equations and inverse preconditioners Chehab,Jean-Paul matrix differential equation numerical schemes numerical linear algebra preconditioning |
title_short |
Matrix differential equations and inverse preconditioners |
title_full |
Matrix differential equations and inverse preconditioners |
title_fullStr |
Matrix differential equations and inverse preconditioners |
title_full_unstemmed |
Matrix differential equations and inverse preconditioners |
title_sort |
Matrix differential equations and inverse preconditioners |
author |
Chehab,Jean-Paul |
author_facet |
Chehab,Jean-Paul |
author_role |
author |
dc.contributor.author.fl_str_mv |
Chehab,Jean-Paul |
dc.subject.por.fl_str_mv |
matrix differential equation numerical schemes numerical linear algebra preconditioning |
topic |
matrix differential equation numerical schemes numerical linear algebra preconditioning |
description |
In this article, we propose to model the inverse of a given matrix as the state of a proper first order matrix differential equation. The inverse can correspond to a finite value of the independent variable or can be reached as a steady state. In both cases we derive corresponding dynamical systems and establish stability and convergence results. The application of a numerical time marching scheme is then proposed to compute an approximation of the inverse. The study of the underlying schemes can be done by using tools of numerical analysis instead of linear algebra techniques only. With our approach, we recover some known schemes but also introduce new ones. We derive in addition a masked dynamical system for computing sparse inverse approximations. Finally we give numerical results that illustrate the validity of our approach. |
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=S1807-03022007000100005 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022007000100005 |
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.26 n.1 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 |
_version_ |
1754734889829138432 |