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

In a recent paper (Cucker et al., 2008 [8]) 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 m...

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Autores principales: Cucker, F., Krick, T., Malajovich, G., Wschebor, M.
Formato: JOUR
Materias:
Average-case analysis
Condition numbers
Finite precision
Rice formula
Zero counting
Number theory
Random variables
Algorithms
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_01968858_v48_n1_p215_Cucker
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_01968858_v48_n1_p215_Cucker
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spelling todo:paper_01968858_v48_n1_p215_Cucker2023-10-03T15:09:49Z A numerical algorithm for zero counting. III: Randomization and condition Cucker, F. Krick, T. Malajovich, G. Wschebor, M. Average-case analysis Condition numbers Finite precision Rice formula Zero counting Average-case analysis Condition numbers Finite precision Rice formula Zero counting Number theory Random variables Algorithms In a recent paper (Cucker et al., 2008 [8]) 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(logκ(f)). © 2011 Elsevier Inc. All rights reserved. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_01968858_v48_n1_p215_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 Average-case analysis
Condition numbers
Finite precision
Rice formula
Zero counting
Average-case analysis
Condition numbers
Finite precision
Rice formula
Zero counting
Number theory
Random variables
Algorithms
spellingShingle Average-case analysis
Condition numbers
Finite precision
Rice formula
Zero counting
Average-case analysis
Condition numbers
Finite precision
Rice formula
Zero counting
Number theory
Random variables
Algorithms
Cucker, F.
Krick, T.
Malajovich, G.
Wschebor, M.
A numerical algorithm for zero counting. III: Randomization and condition
topic_facet Average-case analysis
Condition numbers
Finite precision
Rice formula
Zero counting
Average-case analysis
Condition numbers
Finite precision
Rice formula
Zero counting
Number theory
Random variables
Algorithms
description In a recent paper (Cucker et al., 2008 [8]) 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(logκ(f)). © 2011 Elsevier Inc. All rights reserved.
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. III: Randomization and condition
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 numerical algorithm for zero counting. iii: randomization and condition
url http://hdl.handle.net/20.500.12110/paper_01968858_v48_n1_p215_Cucker
work_keys_str_mv AT cuckerf anumericalalgorithmforzerocountingiiirandomizationandcondition
AT krickt anumericalalgorithmforzerocountingiiirandomizationandcondition
AT malajovichg anumericalalgorithmforzerocountingiiirandomizationandcondition
AT wscheborm anumericalalgorithmforzerocountingiiirandomizationandcondition
AT cuckerf numericalalgorithmforzerocountingiiirandomizationandcondition
AT krickt numericalalgorithmforzerocountingiiirandomizationandcondition
AT malajovichg numericalalgorithmforzerocountingiiirandomizationandcondition
AT wscheborm numericalalgorithmforzerocountingiiirandomizationandcondition
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