A Numerical Algorithm for Zero Counting. II: Distance to Ill-posedness and Smoothed Analysis

Details 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

2009-09-22

arxiv.org/abs/0909.4101v1

Journal of Fixed Point Theory and Applications 6 No 2, pp 285-294 (Dec. 2009)

Computer Science

Numerical Analysis

Scientific paper

10.1007/s11784-009-0127-4

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.

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