A Numerical Algorithm for Zero Counting. II: Distance to Ill-posedness and Smoothed Analysis. (arXiv:0909.4101v1 [cs.NA])

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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Original source : http://arxiv.org/abs/0909.4101...