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
- Institución
- Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
- OAI Identificador
- paperaa:paper_03043975_v411_n44-46_p3894_Herrero
Ver los metadatos del registro completo
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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/ar2025-09-29T13:42:54Zpaperaa: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:18962025-09-29 13:42:56.157Biblioteca 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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1844618735090925568 |
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13.070432 |