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

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 a...

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Detalles Bibliográficos
Autores principales:	Cucker, F., Krick, T., Malajovich, G., Wschebor, M.
Formato:	JOUR
Materias:	Condition numbers Polynomial systems Smoothed analysis Zero counting
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_16617738_v6_n2_p285_Cucker
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_16617738_v6_n2_p285_Cucker
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spelling	todo:paper_16617738_v6_n2_p285_Cucker2023-10-03T16:28:42Z A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis Cucker, F. Krick, T. Malajovich, G. Wschebor, M. Condition numbers Polynomial systems Smoothed analysis Zero counting 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. © 2009 Birkhäuser Verlag Basel/Switzerland. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_16617738_v6_n2_p285_Cucker
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 numbers Polynomial systems Smoothed analysis Zero counting
spellingShingle	Condition numbers Polynomial systems Smoothed analysis Zero counting Cucker, F. Krick, T. Malajovich, G. Wschebor, M. A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis
topic_facet	Condition numbers Polynomial systems Smoothed analysis Zero counting
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. © 2009 Birkhäuser Verlag Basel/Switzerland.
format	JOUR
author	Cucker, F. Krick, T. Malajovich, G. Wschebor, M.
author_facet	Cucker, F. Krick, T. Malajovich, G. Wschebor, M.
author_sort	Cucker, F.
title	A numerical algorithm for zero counting. II: Distance to ill-posedness and 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	numerical algorithm for zero counting. ii: distance to ill-posedness and smoothed analysis
url	http://hdl.handle.net/20.500.12110/paper_16617738_v6_n2_p285_Cucker
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A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis

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