Bipolar varieties and real solving of a singular polynomial equation

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We introduce the concept of a bipolar variety of a real algebraic hypersurface. This notion is then used for the design and complexity estimations of a novel type of algorithms that finds algebraic sample points for the connected components of a singular real hypersurface. The complexity of these al...

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Autores principales: Bank, B., Giusti, M., Heint, J., Pardo, L.M.
Formato: JOUR
Materias:
Polar varieties
Real polynomial equation solving
Singular hypersurface
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_18893066_v2_n1_p65_Bank
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_18893066_v2_n1_p65_Bank
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spelling todo:paper_18893066_v2_n1_p65_Bank2023-10-03T16:34:24Z Bipolar varieties and real solving of a singular polynomial equation Bank, B. Giusti, M. Heint, J. Pardo, L.M. Polar varieties Real polynomial equation solving Singular hypersurface We introduce the concept of a bipolar variety of a real algebraic hypersurface. This notion is then used for the design and complexity estimations of a novel type of algorithms that finds algebraic sample points for the connected components of a singular real hypersurface. The complexity of these algorithms is polynomial in the maximal geometric degree of the bipolar varieties of the given hypersurface and in this sense intrinsic. © 2010 Universidad de Jaén. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_18893066_v2_n1_p65_Bank
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Polar varieties
Real polynomial equation solving
Singular hypersurface
spellingShingle Polar varieties
Real polynomial equation solving
Singular hypersurface
Bank, B.
Giusti, M.
Heint, J.
Pardo, L.M.
Bipolar varieties and real solving of a singular polynomial equation
topic_facet Polar varieties
Real polynomial equation solving
Singular hypersurface
description We introduce the concept of a bipolar variety of a real algebraic hypersurface. This notion is then used for the design and complexity estimations of a novel type of algorithms that finds algebraic sample points for the connected components of a singular real hypersurface. The complexity of these algorithms is polynomial in the maximal geometric degree of the bipolar varieties of the given hypersurface and in this sense intrinsic. © 2010 Universidad de Jaén.
format JOUR
author Bank, B.
Giusti, M.
Heint, J.
Pardo, L.M.
author_facet Bank, B.
Giusti, M.
Heint, J.
Pardo, L.M.
author_sort Bank, B.
title Bipolar varieties and real solving of a singular polynomial equation
title_short Bipolar varieties and real solving of a singular polynomial equation
title_full Bipolar varieties and real solving of a singular polynomial equation
title_fullStr Bipolar varieties and real solving of a singular polynomial equation
title_full_unstemmed Bipolar varieties and real solving of a singular polynomial equation
title_sort bipolar varieties and real solving of a singular polynomial equation
url http://hdl.handle.net/20.500.12110/paper_18893066_v2_n1_p65_Bank
work_keys_str_mv AT bankb bipolarvarietiesandrealsolvingofasingularpolynomialequation
AT giustim bipolarvarietiesandrealsolvingofasingularpolynomialequation
AT heintj bipolarvarietiesandrealsolvingofasingularpolynomialequation
AT pardolm bipolarvarietiesandrealsolvingofasingularpolynomialequation
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