Computing isolated roots of sparse polynomial systems in affine space

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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 squar...

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Detalles Bibliográficos
Autores principales: Herrero, M.I., Jeronimo, G., Sabia, J.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2010
Materias:
Algorithms
Complexity
Sparse polynomial systems
Affine space
Combinatorial structures
Finite set
Geometric resolution
Homotopies
Numerical algorithms
Pre-processing
Probabilistic algorithm
Sparse polynomials
System supports
Systems of equations
Topology
Polynomials
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_03043975_v411_n44-46_p3894_Herrero
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paperaa:paper_03043975_v411_n44-46_p3894_Herrero
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spelling paperaa:paper_03043975_v411_n44-46_p3894_Herrero2023-06-12T16:47:27Z Computing isolated roots of sparse polynomial systems in affine space Theor Comput Sci 2010;411(44-46):3894-3904 Herrero, M.I. Jeronimo, G. Sabia, J. 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 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. 2010 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03043975_v411_n44-46_p3894_Herrero
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
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
spellingShingle 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
Herrero, M.I.
Jeronimo, G.
Sabia, J.
Computing isolated roots of sparse polynomial systems in affine space
topic_facet 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
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.
format Artículo
Artículo
publishedVersion
author Herrero, M.I.
Jeronimo, G.
Sabia, J.
author_facet Herrero, M.I.
Jeronimo, G.
Sabia, J.
author_sort Herrero, M.I.
title Computing isolated roots of sparse polynomial systems in affine space
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
publishDate 2010
url http://hdl.handle.net/20.500.12110/paper_03043975_v411_n44-46_p3894_Herrero
work_keys_str_mv AT herreromi computingisolatedrootsofsparsepolynomialsystemsinaffinespace
AT jeronimog computingisolatedrootsofsparsepolynomialsystemsinaffinespace
AT sabiaj computingisolatedrootsofsparsepolynomialsystemsinaffinespace
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