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

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...

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Veröffentlicht in:Journal of fixed point theory and applications 2009-12, Vol.6 (2), p.285-294
Hauptverfasser: Cucker, Felipe, Krick, Teresa, Malajovich, Gregorio, Wschebor, Mario
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
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Zusammenfassung:. 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.
ISSN:1661-7738
1661-7746
DOI:10.1007/s11784-009-0127-4