Computing isolated roots of sparse polynomial systems in affine space

Autores
Herrero, M.I.; Jeronimo, G.; Sabia, J.
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. © 2010 Elsevier B.V. All rights reserved.
Fil:Herrero, M.I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Jeronimo, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Sabia, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fuente
Theor Comput Sci 2010;411(44-46):3894-3904
Materia
Algorithms
Complexity
Sparse polynomial systems
Affine space
Combinatorial structures
Complexity
Finite set
Geometric resolution
Homotopies
Numerical algorithms
Pre-processing
Probabilistic algorithm
Sparse polynomials
System supports
Systems of equations
Algorithms
Topology
Polynomials
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/2.5/ar
Repositorio
Biblioteca Digital (UBA-FCEN)
Institución
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
OAI Identificador
paperaa:paper_03043975_v411_n44-46_p3894_Herrero
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oai_identifier_str paperaa:paper_03043975_v411_n44-46_p3894_Herrero
network_acronym_str BDUBAFCEN
repository_id_str 1896
network_name_str Biblioteca Digital (UBA-FCEN)
spelling Computing isolated roots of sparse polynomial systems in affine spaceHerrero, M.I.Jeronimo, G.Sabia, J.AlgorithmsComplexitySparse polynomial systemsAffine spaceCombinatorial structuresComplexityFinite setGeometric resolutionHomotopiesNumerical algorithmsPre-processingProbabilistic algorithmSparse polynomialsSystem supportsSystems of equationsAlgorithmsTopologyPolynomialsWe 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. © 2010 Elsevier B.V. All rights reserved.Fil:Herrero, M.I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Jeronimo, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Sabia, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2010info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_03043975_v411_n44-46_p3894_HerreroTheor Comput Sci 2010;411(44-46):3894-3904reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-10-16T09:30:04Zpaperaa:paper_03043975_v411_n44-46_p3894_HerreroInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-10-16 09:30:05.544Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
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, M.I.
Algorithms
Complexity
Sparse polynomial systems
Affine space
Combinatorial structures
Complexity
Finite set
Geometric resolution
Homotopies
Numerical algorithms
Pre-processing
Probabilistic algorithm
Sparse polynomials
System supports
Systems of equations
Algorithms
Topology
Polynomials
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, M.I.
Jeronimo, G.
Sabia, J.
author Herrero, M.I.
author_facet Herrero, M.I.
Jeronimo, G.
Sabia, J.
author_role author
author2 Jeronimo, G.
Sabia, J.
author2_role author
author
dc.subject.none.fl_str_mv Algorithms
Complexity
Sparse polynomial systems
Affine space
Combinatorial structures
Complexity
Finite set
Geometric resolution
Homotopies
Numerical algorithms
Pre-processing
Probabilistic algorithm
Sparse polynomials
System supports
Systems of equations
Algorithms
Topology
Polynomials
topic Algorithms
Complexity
Sparse polynomial systems
Affine space
Combinatorial structures
Complexity
Finite set
Geometric resolution
Homotopies
Numerical algorithms
Pre-processing
Probabilistic algorithm
Sparse polynomials
System supports
Systems of equations
Algorithms
Topology
Polynomials
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. © 2010 Elsevier B.V. All rights reserved.
Fil:Herrero, M.I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Jeronimo, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Sabia, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; 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. © 2010 Elsevier B.V. All rights reserved.
publishDate 2010
dc.date.none.fl_str_mv 2010
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/20.500.12110/paper_03043975_v411_n44-46_p3894_Herrero
url http://hdl.handle.net/20.500.12110/paper_03043975_v411_n44-46_p3894_Herrero
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv Theor Comput Sci 2010;411(44-46):3894-3904
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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score 12.712165

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