Numeric vs. symbolic homotopy algorithms in polynomial system solving: A case study

Autores
De Leo, M.; Dratman, E.; Matera, G.
Año de publicación
2005
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider a family of polynomial systems which arises in the analysis of the stationary solutions of a standard discretization of certain semi-linear second-order parabolic partial differential equations. We prove that this family is well-conditioned from the numeric point of view, and ill-conditioned from the symbolic point of view. We exhibit a polynomial-time numeric algorithm solving any member of this family, which significantly contrasts the exponential behavior of all known symbolic algorithms solving a generic instance of this family of systems. © 2005 Elsevier Inc. All rights reserved.
Fil:De Leo, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Dratman, E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Matera, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fuente
J. Complexity 2005;21(4):502-531
Materia
Complexity
Conditioning
Homotopy algorithms
Polynomial system solving
Semi-linear parabolic problems
Stationary solutions
Algorithms
Boundary value problems
Mathematical models
Matrix algebra
Partial differential equations
Polynomials
Set theory
Homotopy algorithms
Polynomial system solving
Semi linear parabolic problems
Stationary solutions
Computational complexity
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_0885064X_v21_n4_p502_DeLeo
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oai_identifier_str paperaa:paper_0885064X_v21_n4_p502_DeLeo
network_acronym_str BDUBAFCEN
repository_id_str 1896
network_name_str Biblioteca Digital (UBA-FCEN)
spelling Numeric vs. symbolic homotopy algorithms in polynomial system solving: A case studyDe Leo, M.Dratman, E.Matera, G.ComplexityConditioningHomotopy algorithmsPolynomial system solvingSemi-linear parabolic problemsStationary solutionsAlgorithmsBoundary value problemsMathematical modelsMatrix algebraPartial differential equationsPolynomialsSet theoryHomotopy algorithmsPolynomial system solvingSemi linear parabolic problemsStationary solutionsComputational complexityWe consider a family of polynomial systems which arises in the analysis of the stationary solutions of a standard discretization of certain semi-linear second-order parabolic partial differential equations. We prove that this family is well-conditioned from the numeric point of view, and ill-conditioned from the symbolic point of view. We exhibit a polynomial-time numeric algorithm solving any member of this family, which significantly contrasts the exponential behavior of all known symbolic algorithms solving a generic instance of this family of systems. © 2005 Elsevier Inc. All rights reserved.Fil:De Leo, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Dratman, E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Matera, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2005info: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_0885064X_v21_n4_p502_DeLeoJ. Complexity 2005;21(4):502-531reponame: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/ar2025-09-29T13:43:00Zpaperaa:paper_0885064X_v21_n4_p502_DeLeoInstitucionalhttps://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 13:43:01.558Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv Numeric vs. symbolic homotopy algorithms in polynomial system solving: A case study
title Numeric vs. symbolic homotopy algorithms in polynomial system solving: A case study
spellingShingle Numeric vs. symbolic homotopy algorithms in polynomial system solving: A case study
De Leo, M.
Complexity
Conditioning
Homotopy algorithms
Polynomial system solving
Semi-linear parabolic problems
Stationary solutions
Algorithms
Boundary value problems
Mathematical models
Matrix algebra
Partial differential equations
Polynomials
Set theory
Homotopy algorithms
Polynomial system solving
Semi linear parabolic problems
Stationary solutions
Computational complexity
title_short Numeric vs. symbolic homotopy algorithms in polynomial system solving: A case study
title_full Numeric vs. symbolic homotopy algorithms in polynomial system solving: A case study
title_fullStr Numeric vs. symbolic homotopy algorithms in polynomial system solving: A case study
title_full_unstemmed Numeric vs. symbolic homotopy algorithms in polynomial system solving: A case study
title_sort Numeric vs. symbolic homotopy algorithms in polynomial system solving: A case study
dc.creator.none.fl_str_mv De Leo, M.
Dratman, E.
Matera, G.
author De Leo, M.
author_facet De Leo, M.
Dratman, E.
Matera, G.
author_role author
author2 Dratman, E.
Matera, G.
author2_role author
author
dc.subject.none.fl_str_mv Complexity
Conditioning
Homotopy algorithms
Polynomial system solving
Semi-linear parabolic problems
Stationary solutions
Algorithms
Boundary value problems
Mathematical models
Matrix algebra
Partial differential equations
Polynomials
Set theory
Homotopy algorithms
Polynomial system solving
Semi linear parabolic problems
Stationary solutions
Computational complexity
topic Complexity
Conditioning
Homotopy algorithms
Polynomial system solving
Semi-linear parabolic problems
Stationary solutions
Algorithms
Boundary value problems
Mathematical models
Matrix algebra
Partial differential equations
Polynomials
Set theory
Homotopy algorithms
Polynomial system solving
Semi linear parabolic problems
Stationary solutions
Computational complexity
dc.description.none.fl_txt_mv We consider a family of polynomial systems which arises in the analysis of the stationary solutions of a standard discretization of certain semi-linear second-order parabolic partial differential equations. We prove that this family is well-conditioned from the numeric point of view, and ill-conditioned from the symbolic point of view. We exhibit a polynomial-time numeric algorithm solving any member of this family, which significantly contrasts the exponential behavior of all known symbolic algorithms solving a generic instance of this family of systems. © 2005 Elsevier Inc. All rights reserved.
Fil:De Leo, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Dratman, E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Matera, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
description We consider a family of polynomial systems which arises in the analysis of the stationary solutions of a standard discretization of certain semi-linear second-order parabolic partial differential equations. We prove that this family is well-conditioned from the numeric point of view, and ill-conditioned from the symbolic point of view. We exhibit a polynomial-time numeric algorithm solving any member of this family, which significantly contrasts the exponential behavior of all known symbolic algorithms solving a generic instance of this family of systems. © 2005 Elsevier Inc. All rights reserved.
publishDate 2005
dc.date.none.fl_str_mv 2005
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_0885064X_v21_n4_p502_DeLeo
url http://hdl.handle.net/20.500.12110/paper_0885064X_v21_n4_p502_DeLeo
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 J. Complexity 2005;21(4):502-531
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 13.070432

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