Computing isolated roots of sparse polynomial systems in affine space

Autores
Herrero, Maria Isabel; Jeronimo, Gabriela Tali; Sabia, Juan Vicente Rafael
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We present a symbolic probabilistic algorithm to compute the isolated roots in Cn of sparse polynomial equation systems. As some already known numerical algorithms solving this task, our procedure is based on polyhedral deformations and homotopies, but it amounts to solving a smaller number of square systems of equations and in fewer variables. The output of the algorithm is a geometric resolution of a finite set of points including the isolated roots of the system. The complexity is polynomial in the size of the combinatorial structure of the system supports up to a pre-processing yielding the mixed cells in a subdivision of the family of these supports.
Fil: Herrero, Maria Isabel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Jeronimo, Gabriela Tali. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Sabia, Juan Vicente Rafael. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Algorithms
Complexity
Sparse Polynomial Systems
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/67998
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/67998
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Computing isolated roots of sparse polynomial systems in affine spaceHerrero, Maria IsabelJeronimo, Gabriela TaliSabia, Juan Vicente RafaelAlgorithmsComplexitySparse Polynomial Systemshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We present a symbolic probabilistic algorithm to compute the isolated roots in Cn of sparse polynomial equation systems. As some already known numerical algorithms solving this task, our procedure is based on polyhedral deformations and homotopies, but it amounts to solving a smaller number of square systems of equations and in fewer variables. The output of the algorithm is a geometric resolution of a finite set of points including the isolated roots of the system. The complexity is polynomial in the size of the combinatorial structure of the system supports up to a pre-processing yielding the mixed cells in a subdivision of the family of these supports.Fil: Herrero, Maria Isabel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Jeronimo, Gabriela Tali. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Sabia, Juan Vicente Rafael. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaElsevier Science2010-10info: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/11336/67998Herrero, Maria Isabel; Jeronimo, Gabriela Tali; Sabia, Juan Vicente Rafael; Computing isolated roots of sparse polynomial systems in affine space; Elsevier Science; Theoretical Computer Science; 411; 44-46; 10-2010; 3894-39040304-3975CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0304397510004019info:eu-repo/semantics/altIdentifier/doi/10.1016/j.tcs.2010.07.015info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:52:44Zoai:ri.conicet.gov.ar:11336/67998instacron: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:34982025-09-29 09:52:44.97CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Computing isolated roots of sparse polynomial systems in affine space
title Computing isolated roots of sparse polynomial systems in affine space
spellingShingle Computing isolated roots of sparse polynomial systems in affine space
Herrero, Maria Isabel
Algorithms
Complexity
Sparse Polynomial Systems
title_short Computing isolated roots of sparse polynomial systems in affine space
title_full Computing isolated roots of sparse polynomial systems in affine space
title_fullStr Computing isolated roots of sparse polynomial systems in affine space
title_full_unstemmed Computing isolated roots of sparse polynomial systems in affine space
title_sort Computing isolated roots of sparse polynomial systems in affine space
dc.creator.none.fl_str_mv Herrero, Maria Isabel
Jeronimo, Gabriela Tali
Sabia, Juan Vicente Rafael
author Herrero, Maria Isabel
author_facet Herrero, Maria Isabel
Jeronimo, Gabriela Tali
Sabia, Juan Vicente Rafael
author_role author
author2 Jeronimo, Gabriela Tali
Sabia, Juan Vicente Rafael
author2_role author
author
dc.subject.none.fl_str_mv Algorithms
Complexity
Sparse Polynomial Systems
topic Algorithms
Complexity
Sparse Polynomial Systems
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 present a symbolic probabilistic algorithm to compute the isolated roots in Cn of sparse polynomial equation systems. As some already known numerical algorithms solving this task, our procedure is based on polyhedral deformations and homotopies, but it amounts to solving a smaller number of square systems of equations and in fewer variables. The output of the algorithm is a geometric resolution of a finite set of points including the isolated roots of the system. The complexity is polynomial in the size of the combinatorial structure of the system supports up to a pre-processing yielding the mixed cells in a subdivision of the family of these supports.
Fil: Herrero, Maria Isabel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Jeronimo, Gabriela Tali. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Sabia, Juan Vicente Rafael. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We present a symbolic probabilistic algorithm to compute the isolated roots in Cn of sparse polynomial equation systems. As some already known numerical algorithms solving this task, our procedure is based on polyhedral deformations and homotopies, but it amounts to solving a smaller number of square systems of equations and in fewer variables. The output of the algorithm is a geometric resolution of a finite set of points including the isolated roots of the system. The complexity is polynomial in the size of the combinatorial structure of the system supports up to a pre-processing yielding the mixed cells in a subdivision of the family of these supports.
publishDate 2010
dc.date.none.fl_str_mv 2010-10
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/11336/67998
Herrero, Maria Isabel; Jeronimo, Gabriela Tali; Sabia, Juan Vicente Rafael; Computing isolated roots of sparse polynomial systems in affine space; Elsevier Science; Theoretical Computer Science; 411; 44-46; 10-2010; 3894-3904
0304-3975
CONICET Digital
CONICET
url http://hdl.handle.net/11336/67998
identifier_str_mv Herrero, Maria Isabel; Jeronimo, Gabriela Tali; Sabia, Juan Vicente Rafael; Computing isolated roots of sparse polynomial systems in affine space; Elsevier Science; Theoretical Computer Science; 411; 44-46; 10-2010; 3894-3904
0304-3975
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0304397510004019
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.tcs.2010.07.015
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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
_version_ 1844613616323526656
score 13.070432

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