Extensions of incomplete oblique projections method for solving rank-deficient least-squares problems

Autores
Scolnik, Hugo Daniel; Echebest, Nélida Ester; Guardarucci, María Teresa
Año de publicación
2009
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The aim of this paper is to extend the applicability of an algorithm for solving inconsistent linear systems to the rank-deficient case, by employing incomplete projections onto the set of solutions of the augmented system Ax-r = b. The extended algorithm converges to the unique minimal norm solution of the least squares solutions. For that purpose, incomplete oblique projections are used, defined by means of matrices that penalize the norm of the residuals. The theoretical properties of the new algorithm are analyzed, and numerical experiences are presented comparing its performance with some well-known projection methods.
Facultad de Ciencias Exactas
Facultad de Ingeniería
Materia
Ciencias Exactas
Incomplete oblique projections
Minimal norm solution
Rank-deficient least-squares problems
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/82673
Acceder
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network_acronym_str SEDICI
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network_name_str SEDICI (UNLP)
spelling Extensions of incomplete oblique projections method for solving rank-deficient least-squares problemsScolnik, Hugo DanielEchebest, Nélida EsterGuardarucci, María TeresaCiencias ExactasIncomplete oblique projectionsMinimal norm solutionRank-deficient least-squares problemsThe aim of this paper is to extend the applicability of an algorithm for solving inconsistent linear systems to the rank-deficient case, by employing incomplete projections onto the set of solutions of the augmented system Ax-r = b. The extended algorithm converges to the unique minimal norm solution of the least squares solutions. For that purpose, incomplete oblique projections are used, defined by means of matrices that penalize the norm of the residuals. The theoretical properties of the new algorithm are analyzed, and numerical experiences are presented comparing its performance with some well-known projection methods.Facultad de Ciencias ExactasFacultad de Ingeniería2009info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf175-191http://sedici.unlp.edu.ar/handle/10915/82673enginfo:eu-repo/semantics/altIdentifier/issn/1547-5816info:eu-repo/semantics/altIdentifier/doi/10.3934/jimo.2009.5.175info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-17T09:58:19Zoai:sedici.unlp.edu.ar:10915/82673Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-17 09:58:19.913SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Extensions of incomplete oblique projections method for solving rank-deficient least-squares problems
title Extensions of incomplete oblique projections method for solving rank-deficient least-squares problems
spellingShingle Extensions of incomplete oblique projections method for solving rank-deficient least-squares problems
Scolnik, Hugo Daniel
Ciencias Exactas
Incomplete oblique projections
Minimal norm solution
Rank-deficient least-squares problems
title_short Extensions of incomplete oblique projections method for solving rank-deficient least-squares problems
title_full Extensions of incomplete oblique projections method for solving rank-deficient least-squares problems
title_fullStr Extensions of incomplete oblique projections method for solving rank-deficient least-squares problems
title_full_unstemmed Extensions of incomplete oblique projections method for solving rank-deficient least-squares problems
title_sort Extensions of incomplete oblique projections method for solving rank-deficient least-squares problems
dc.creator.none.fl_str_mv Scolnik, Hugo Daniel
Echebest, Nélida Ester
Guardarucci, María Teresa
author Scolnik, Hugo Daniel
author_facet Scolnik, Hugo Daniel
Echebest, Nélida Ester
Guardarucci, María Teresa
author_role author
author2 Echebest, Nélida Ester
Guardarucci, María Teresa
author2_role author
author
dc.subject.none.fl_str_mv Ciencias Exactas
Incomplete oblique projections
Minimal norm solution
Rank-deficient least-squares problems
topic Ciencias Exactas
Incomplete oblique projections
Minimal norm solution
Rank-deficient least-squares problems
dc.description.none.fl_txt_mv The aim of this paper is to extend the applicability of an algorithm for solving inconsistent linear systems to the rank-deficient case, by employing incomplete projections onto the set of solutions of the augmented system Ax-r = b. The extended algorithm converges to the unique minimal norm solution of the least squares solutions. For that purpose, incomplete oblique projections are used, defined by means of matrices that penalize the norm of the residuals. The theoretical properties of the new algorithm are analyzed, and numerical experiences are presented comparing its performance with some well-known projection methods.
Facultad de Ciencias Exactas
Facultad de Ingeniería
description The aim of this paper is to extend the applicability of an algorithm for solving inconsistent linear systems to the rank-deficient case, by employing incomplete projections onto the set of solutions of the augmented system Ax-r = b. The extended algorithm converges to the unique minimal norm solution of the least squares solutions. For that purpose, incomplete oblique projections are used, defined by means of matrices that penalize the norm of the residuals. The theoretical properties of the new algorithm are analyzed, and numerical experiences are presented comparing its performance with some well-known projection methods.
publishDate 2009
dc.date.none.fl_str_mv 2009
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/82673
url http://sedici.unlp.edu.ar/handle/10915/82673
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/1547-5816
info:eu-repo/semantics/altIdentifier/doi/10.3934/jimo.2009.5.175
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
175-191
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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