A numerical algorithm for zero counting. III: Randomization and condition

Autores
Cucker, Felipe; Krick, Teresa Elena Genoveva; Malajovich, Gregorio; Wschebor, Mario
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In a recent paper [7] we analyzed a numerical algorithm for computing the number of real zeros of a polynomial system. The analysis relied on a condition number κ(f) for the input system f. In this paper we look at κ(f) as a random variable derived from imposing a probability measure on the space of polynomial systems and give bounds for both the tail P{κ(f) > a} and the expected value E(log κ(f)).
Fil: Cucker, Felipe. City University of Hong Kong; Hong Kong
Fil: Krick, Teresa Elena Genoveva. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Malajovich, Gregorio. Universidade Federal do Rio de Janeiro; Brasil
Fil: Wschebor, Mario. Universidad de la República; Uruguay
Materia
Zero-counting
Finite-precision
Condition numbers
Average-case analysis
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/19996
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/19996
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A numerical algorithm for zero counting. III: Randomization and conditionCucker, FelipeKrick, Teresa Elena GenovevaMalajovich, GregorioWschebor, MarioZero-countingFinite-precisionCondition numbersAverage-case analysishttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In a recent paper [7] we analyzed a numerical algorithm for computing the number of real zeros of a polynomial system. The analysis relied on a condition number κ(f) for the input system f. In this paper we look at κ(f) as a random variable derived from imposing a probability measure on the space of polynomial systems and give bounds for both the tail P{κ(f) > a} and the expected value E(log κ(f)).Fil: Cucker, Felipe. City University of Hong Kong; Hong KongFil: Krick, Teresa Elena Genoveva. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Malajovich, Gregorio. Universidade Federal do Rio de Janeiro; BrasilFil: Wschebor, Mario. Universidad de la República; UruguayElsevier2012-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/19996Cucker, Felipe; Krick, Teresa Elena Genoveva; Malajovich, Gregorio; Wschebor, Mario; A numerical algorithm for zero counting. III: Randomization and condition; Elsevier; Advances In Applied Mathematics; 48; 1; 1-2012; 215-2480196-8858CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.aam.2011.07.001info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0196885811000728info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1007.1597info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T09:49:00Zoai:ri.conicet.gov.ar:11336/19996instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-11-05 09:49:01.072CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A numerical algorithm for zero counting. III: Randomization and condition
title A numerical algorithm for zero counting. III: Randomization and condition
spellingShingle A numerical algorithm for zero counting. III: Randomization and condition
Cucker, Felipe
Zero-counting
Finite-precision
Condition numbers
Average-case analysis
title_short A numerical algorithm for zero counting. III: Randomization and condition
title_full A numerical algorithm for zero counting. III: Randomization and condition
title_fullStr A numerical algorithm for zero counting. III: Randomization and condition
title_full_unstemmed A numerical algorithm for zero counting. III: Randomization and condition
title_sort A numerical algorithm for zero counting. III: Randomization and condition
dc.creator.none.fl_str_mv Cucker, Felipe
Krick, Teresa Elena Genoveva
Malajovich, Gregorio
Wschebor, Mario
author Cucker, Felipe
author_facet Cucker, Felipe
Krick, Teresa Elena Genoveva
Malajovich, Gregorio
Wschebor, Mario
author_role author
author2 Krick, Teresa Elena Genoveva
Malajovich, Gregorio
Wschebor, Mario
author2_role author
author
author
dc.subject.none.fl_str_mv Zero-counting
Finite-precision
Condition numbers
Average-case analysis
topic Zero-counting
Finite-precision
Condition numbers
Average-case analysis
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In a recent paper [7] we analyzed a numerical algorithm for computing the number of real zeros of a polynomial system. The analysis relied on a condition number κ(f) for the input system f. In this paper we look at κ(f) as a random variable derived from imposing a probability measure on the space of polynomial systems and give bounds for both the tail P{κ(f) > a} and the expected value E(log κ(f)).
Fil: Cucker, Felipe. City University of Hong Kong; Hong Kong
Fil: Krick, Teresa Elena Genoveva. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Malajovich, Gregorio. Universidade Federal do Rio de Janeiro; Brasil
Fil: Wschebor, Mario. Universidad de la República; Uruguay
description In a recent paper [7] we analyzed a numerical algorithm for computing the number of real zeros of a polynomial system. The analysis relied on a condition number κ(f) for the input system f. In this paper we look at κ(f) as a random variable derived from imposing a probability measure on the space of polynomial systems and give bounds for both the tail P{κ(f) > a} and the expected value E(log κ(f)).
publishDate 2012
dc.date.none.fl_str_mv 2012-01
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/11336/19996
Cucker, Felipe; Krick, Teresa Elena Genoveva; Malajovich, Gregorio; Wschebor, Mario; A numerical algorithm for zero counting. III: Randomization and condition; Elsevier; Advances In Applied Mathematics; 48; 1; 1-2012; 215-248
0196-8858
CONICET Digital
CONICET
url http://hdl.handle.net/11336/19996
identifier_str_mv Cucker, Felipe; Krick, Teresa Elena Genoveva; Malajovich, Gregorio; Wschebor, Mario; A numerical algorithm for zero counting. III: Randomization and condition; Elsevier; Advances In Applied Mathematics; 48; 1; 1-2012; 215-248
0196-8858
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aam.2011.07.001
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0196885811000728
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1007.1597
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1847977180474114048
score 13.084122

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