Solving a sparse system using linear algebra

Autores
Massri, Cesar Dario
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We give a new theoretical tool to solve sparse systems with finitely many solutions. It is based on toric varieties and basic linear algebra; eigenvalues, eigenvectors and coefficient matrices. We adapt Eigenvalue theorem and Eigenvector theorem to work with a canonical rectangular matrix (the first Koszul map) and prove that these new theorems serve to solve overdetermined sparse systems and to count the expected number of solutions.
Fil: Massri, Cesar Dario. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
Materia
Multiplication Matrix
Eigenvector
Sparse System
Toric Varieties
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/18860
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Solving a sparse system using linear algebraMassri, Cesar DarioMultiplication MatrixEigenvectorSparse SystemToric Varietieshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We give a new theoretical tool to solve sparse systems with finitely many solutions. It is based on toric varieties and basic linear algebra; eigenvalues, eigenvectors and coefficient matrices. We adapt Eigenvalue theorem and Eigenvector theorem to work with a canonical rectangular matrix (the first Koszul map) and prove that these new theorems serve to solve overdetermined sparse systems and to count the expected number of solutions.Fil: Massri, Cesar Dario. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; ArgentinaElsevier2015-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18860Massri, Cesar Dario; Solving a sparse system using linear algebra; Elsevier; Journal Of Symbolic Computation; 73; 4-2015; 157-1740747-7171CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsc.2015.06.003info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0747717115000449info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1211.3715info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:05:38Zoai:ri.conicet.gov.ar:11336/18860instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:05:39.054CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Solving a sparse system using linear algebra
title Solving a sparse system using linear algebra
spellingShingle Solving a sparse system using linear algebra
Massri, Cesar Dario
Multiplication Matrix
Eigenvector
Sparse System
Toric Varieties
title_short Solving a sparse system using linear algebra
title_full Solving a sparse system using linear algebra
title_fullStr Solving a sparse system using linear algebra
title_full_unstemmed Solving a sparse system using linear algebra
title_sort Solving a sparse system using linear algebra
dc.creator.none.fl_str_mv Massri, Cesar Dario
author Massri, Cesar Dario
author_facet Massri, Cesar Dario
author_role author
dc.subject.none.fl_str_mv Multiplication Matrix
Eigenvector
Sparse System
Toric Varieties
topic Multiplication Matrix
Eigenvector
Sparse System
Toric Varieties
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We give a new theoretical tool to solve sparse systems with finitely many solutions. It is based on toric varieties and basic linear algebra; eigenvalues, eigenvectors and coefficient matrices. We adapt Eigenvalue theorem and Eigenvector theorem to work with a canonical rectangular matrix (the first Koszul map) and prove that these new theorems serve to solve overdetermined sparse systems and to count the expected number of solutions.
Fil: Massri, Cesar Dario. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
description We give a new theoretical tool to solve sparse systems with finitely many solutions. It is based on toric varieties and basic linear algebra; eigenvalues, eigenvectors and coefficient matrices. We adapt Eigenvalue theorem and Eigenvector theorem to work with a canonical rectangular matrix (the first Koszul map) and prove that these new theorems serve to solve overdetermined sparse systems and to count the expected number of solutions.
publishDate 2015
dc.date.none.fl_str_mv 2015-04
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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://hdl.handle.net/11336/18860
Massri, Cesar Dario; Solving a sparse system using linear algebra; Elsevier; Journal Of Symbolic Computation; 73; 4-2015; 157-174
0747-7171
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18860
identifier_str_mv Massri, Cesar Dario; Solving a sparse system using linear algebra; Elsevier; Journal Of Symbolic Computation; 73; 4-2015; 157-174
0747-7171
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsc.2015.06.003
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0747717115000449
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1211.3715
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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