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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2009
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16617738_v6_n2_p285_Cucker http://hdl.handle.net/20.500.12110/paper_16617738_v6_n2_p285_Cucker |
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paper:paper_16617738_v6_n2_p285_Cucker |
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paper:paper_16617738_v6_n2_p285_Cucker2023-06-08T16:25:44Z A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis 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. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16617738_v6_n2_p285_Cucker 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 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. |
| 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 |
| publishDate |
2009 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16617738_v6_n2_p285_Cucker http://hdl.handle.net/20.500.12110/paper_16617738_v6_n2_p285_Cucker |
| _version_ |
1768545115018625024 |