Computing isolated roots of sparse polynomial systems in affine space
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...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2010 |
| País: | Argentina |
| Institución: | Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
| Repositorio: | Biblioteca Digital (UBA-FCEN) |
| Idioma: | inglés |
| OAI Identifier: | paperaa:paper_03043975_v411_n44-46_p3894_Herrero |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_03043975_v411_n44-46_p3894_Herrero |
| Access Level: | acceso abierto |
| Palabra clave: | 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 |
| Sumario: | 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. |
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