On computation of matrix logarithm times a vector

Matrix functions have become a central topic in linear algebra, and many problems of their numerical approximation appear often in scientific computing. This thesis concerns with matrix functions times a vector with a special attention in the matrix logarithm case. In many applications the original...

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Detalles Bibliográficos
Autor: Gimeno Alquézar, Joan
Tipo de recurso: tesis de maestría
Fecha de publicación:2017
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/107140
Acceso en línea:https://hdl.handle.net/2117/107140
Access Level:acceso abierto
Palabra clave:Computer algorithms
Computer programming
Algorismes computacionals
Programació (Ordinadors)
Àrees temàtiques de la UPC::Informàtica
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spelling On computation of matrix logarithm times a vectorGimeno Alquézar, JoanComputer algorithmsComputer programmingAlgorismes computacionalsProgramació (Ordinadors)Àrees temàtiques de la UPC::InformàticaMatrix functions have become a central topic in linear algebra, and many problems of their numerical approximation appear often in scientific computing. This thesis concerns with matrix functions times a vector with a special attention in the matrix logarithm case. In many applications the original matrix may be large, sparse or structured. In this case evaluating the matrix function times a vector by first computing the full matrix function is usually unfeasible, so that it has sense to approximate the solution saving storage and computational time. Looking into the literature in numerical linear algebra, the standard approach for computing the matrix function times a vectors directly is based on a polynomial Krylov subspace approach that only requires matrix–vector products of the original matrix. This project deals with rational Krylov subspace which have been used recently in this context though it was originally presented for eigenvalue problem in the 90s.Universitat Politècnica de CatalunyaOtero Calviño, BeatrizHayami, Ken20172017-07-1120172017-08-25master thesishttp://purl.org/coar/resource_type/c_bdccNAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/masterThesisapplication/pdfhttps://hdl.handle.net/2117/107140reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1071402026-05-27T15:37:01Z
dc.title.none.fl_str_mv On computation of matrix logarithm times a vector
title On computation of matrix logarithm times a vector
spellingShingle On computation of matrix logarithm times a vector
Gimeno Alquézar, Joan
Computer algorithms
Computer programming
Algorismes computacionals
Programació (Ordinadors)
Àrees temàtiques de la UPC::Informàtica
title_short On computation of matrix logarithm times a vector
title_full On computation of matrix logarithm times a vector
title_fullStr On computation of matrix logarithm times a vector
title_full_unstemmed On computation of matrix logarithm times a vector
title_sort On computation of matrix logarithm times a vector
dc.creator.none.fl_str_mv Gimeno Alquézar, Joan
author Gimeno Alquézar, Joan
author_facet Gimeno Alquézar, Joan
author_role author
dc.contributor.none.fl_str_mv Otero Calviño, Beatriz
Hayami, Ken
dc.subject.none.fl_str_mv Computer algorithms
Computer programming
Algorismes computacionals
Programació (Ordinadors)
Àrees temàtiques de la UPC::Informàtica
topic Computer algorithms
Computer programming
Algorismes computacionals
Programació (Ordinadors)
Àrees temàtiques de la UPC::Informàtica
description Matrix functions have become a central topic in linear algebra, and many problems of their numerical approximation appear often in scientific computing. This thesis concerns with matrix functions times a vector with a special attention in the matrix logarithm case. In many applications the original matrix may be large, sparse or structured. In this case evaluating the matrix function times a vector by first computing the full matrix function is usually unfeasible, so that it has sense to approximate the solution saving storage and computational time. Looking into the literature in numerical linear algebra, the standard approach for computing the matrix function times a vectors directly is based on a polynomial Krylov subspace approach that only requires matrix–vector products of the original matrix. This project deals with rational Krylov subspace which have been used recently in this context though it was originally presented for eigenvalue problem in the 90s.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-07-11
2017
2017-08-25
dc.type.none.fl_str_mv master thesis
http://purl.org/coar/resource_type/c_bdcc
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/107140
url https://hdl.handle.net/2117/107140
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universitat Politècnica de Catalunya
publisher.none.fl_str_mv Universitat Politècnica de Catalunya
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
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