A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis

Autores
Cucker, Felipe; Krick, Teresa Elena Genoveva; Malajovich, Gregorio; Wschebor, Mario
Año de publicación
2009
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We show a Condition Number Theorem for the condition number of zero counting for real polynomial systems. That is, we show that this condition number equals the inverse of the normalized distance to the set of ill-posed systems (i.e., those having multiple real zeros). As a consequence, a smoothed analysis of this condition number follows.
Fil: Cucker, Felipe. University of Hong Kong; China
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
POLYNOMIAL SYSTEMS
ZERO COUNTING
CONDITION NUMBERS
SMOOTHED ANALYSIS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/244759
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/244759
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysisCucker, FelipeKrick, Teresa Elena GenovevaMalajovich, GregorioWschebor, MarioPOLYNOMIAL SYSTEMSZERO COUNTINGCONDITION NUMBERSSMOOTHED ANALYSIShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We show a Condition Number Theorem for the condition number of zero counting for real polynomial systems. That is, we show that this condition number equals the inverse of the normalized distance to the set of ill-posed systems (i.e., those having multiple real zeros). As a consequence, a smoothed analysis of this condition number follows.Fil: Cucker, Felipe. University of Hong Kong; ChinaFil: 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; UruguayBirkhauser Verlag Ag2009-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/244759Cucker, Felipe; Krick, Teresa Elena Genoveva; Malajovich, Gregorio; Wschebor, Mario; A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis; Birkhauser Verlag Ag; Journal Of Fixed Point Theory And Applications; 6; 2; 11-2009; 285-2941661-7738CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s11784-009-0127-4info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s11784-009-0127-4info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/0909.4101info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:58:44Zoai:ri.conicet.gov.ar:11336/244759instacron: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:34982025-10-15 14:58:44.964CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis
title A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis
spellingShingle A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis
Cucker, Felipe
POLYNOMIAL SYSTEMS
ZERO COUNTING
CONDITION NUMBERS
SMOOTHED ANALYSIS
title_short A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis
title_full A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis
title_fullStr A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis
title_full_unstemmed A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis
title_sort A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis
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 POLYNOMIAL SYSTEMS
ZERO COUNTING
CONDITION NUMBERS
SMOOTHED ANALYSIS
topic POLYNOMIAL SYSTEMS
ZERO COUNTING
CONDITION NUMBERS
SMOOTHED 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 We show a Condition Number Theorem for the condition number of zero counting for real polynomial systems. That is, we show that this condition number equals the inverse of the normalized distance to the set of ill-posed systems (i.e., those having multiple real zeros). As a consequence, a smoothed analysis of this condition number follows.
Fil: Cucker, Felipe. University of Hong Kong; China
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 We show a Condition Number Theorem for the condition number of zero counting for real polynomial systems. That is, we show that this condition number equals the inverse of the normalized distance to the set of ill-posed systems (i.e., those having multiple real zeros). As a consequence, a smoothed analysis of this condition number follows.
publishDate 2009
dc.date.none.fl_str_mv 2009-11
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/11336/244759
Cucker, Felipe; Krick, Teresa Elena Genoveva; Malajovich, Gregorio; Wschebor, Mario; A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis; Birkhauser Verlag Ag; Journal Of Fixed Point Theory And Applications; 6; 2; 11-2009; 285-294
1661-7738
CONICET Digital
CONICET
url http://hdl.handle.net/11336/244759
identifier_str_mv Cucker, Felipe; Krick, Teresa Elena Genoveva; Malajovich, Gregorio; Wschebor, Mario; A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis; Birkhauser Verlag Ag; Journal Of Fixed Point Theory And Applications; 6; 2; 11-2009; 285-294
1661-7738
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s11784-009-0127-4
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s11784-009-0127-4
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/0909.4101
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Birkhauser Verlag Ag
publisher.none.fl_str_mv Birkhauser Verlag Ag
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_ 1846083128298307584
score 13.22299

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