On the Geometry and Topology of the Solution Variety for Polynomial System Solving

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We study the geometry and topology of the rank stratification for polynomial system solving, i. e., the set of pairs (system, solution) such that the derivative of the system at the solution has a given rank. Our approach is to study the gradient flow of the Frobenius condition number defined on eac...

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Autores principales: Beltrán, C., Shub, M.
Formato: JOUR
Materias:
Condition metric
Condition number
Gradient flow
Homotopy methods
Solution variety
Stratification
Condition numbers
Homotopy method
Polynomial system solving
Number theory
Thermal stratification
Topology
Polynomials
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_16153375_v12_n6_p719_Beltran
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_16153375_v12_n6_p719_Beltran
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spelling todo:paper_16153375_v12_n6_p719_Beltran2023-10-03T16:28:12Z On the Geometry and Topology of the Solution Variety for Polynomial System Solving Beltrán, C. Shub, M. Condition metric Condition number Gradient flow Homotopy methods Solution variety Stratification Condition metric Condition numbers Gradient flow Homotopy method Polynomial system solving Number theory Thermal stratification Topology Polynomials We study the geometry and topology of the rank stratification for polynomial system solving, i. e., the set of pairs (system, solution) such that the derivative of the system at the solution has a given rank. Our approach is to study the gradient flow of the Frobenius condition number defined on each stratum. © 2012 SFoCM. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_16153375_v12_n6_p719_Beltran
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Condition metric
Condition number
Gradient flow
Homotopy methods
Solution variety
Stratification
Condition metric
Condition numbers
Gradient flow
Homotopy method
Polynomial system solving
Number theory
Thermal stratification
Topology
Polynomials
spellingShingle Condition metric
Condition number
Gradient flow
Homotopy methods
Solution variety
Stratification
Condition metric
Condition numbers
Gradient flow
Homotopy method
Polynomial system solving
Number theory
Thermal stratification
Topology
Polynomials
Beltrán, C.
Shub, M.
On the Geometry and Topology of the Solution Variety for Polynomial System Solving
topic_facet Condition metric
Condition number
Gradient flow
Homotopy methods
Solution variety
Stratification
Condition metric
Condition numbers
Gradient flow
Homotopy method
Polynomial system solving
Number theory
Thermal stratification
Topology
Polynomials
description We study the geometry and topology of the rank stratification for polynomial system solving, i. e., the set of pairs (system, solution) such that the derivative of the system at the solution has a given rank. Our approach is to study the gradient flow of the Frobenius condition number defined on each stratum. © 2012 SFoCM.
format JOUR
author Beltrán, C.
Shub, M.
author_facet Beltrán, C.
Shub, M.
author_sort Beltrán, C.
title On the Geometry and Topology of the Solution Variety for Polynomial System Solving
title_short On the Geometry and Topology of the Solution Variety for Polynomial System Solving
title_full On the Geometry and Topology of the Solution Variety for Polynomial System Solving
title_fullStr On the Geometry and Topology of the Solution Variety for Polynomial System Solving
title_full_unstemmed On the Geometry and Topology of the Solution Variety for Polynomial System Solving
title_sort on the geometry and topology of the solution variety for polynomial system solving
url http://hdl.handle.net/20.500.12110/paper_16153375_v12_n6_p719_Beltran
work_keys_str_mv AT beltranc onthegeometryandtopologyofthesolutionvarietyforpolynomialsystemsolving
AT shubm onthegeometryandtopologyofthesolutionvarietyforpolynomialsystemsolving
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