Teresa Krick
A Numerical Algorithm for Zero Counting. III: Randomization and Condition.
Пнд, 07/12/2010 - 15:01 — SomNambulAuthors: Felipe Cucker, Teresa Krick, Gregorio Malajovich, Mario Wschebor
Subjects: Numerical Analysis
AbstractIn a recent paper (Cucker, Krick, Malajovich and Wschebor, A Numerical
Algorithm for Zero Counting. I: Complexity and accuracy, J. Compl.,24:582-605,
2008) we analyzed a numerical algorithm for computing the number of real zeros
of a polynomial system. The analysis relied on a condition number kappa(f) for
the input system f. In this paper, we look at kappa(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{kappa(f) > a} and the expected value E(log
kappa(f)).A Numerical Algorithm for Zero Counting. II: Distance to Ill-posedness and Smoothed Analysis.
Чт, 09/24/2009 - 12:35 — SomNambulAuthors: Felipe Cucker, Teresa Krick, Gregorio Malajovich, Mario Wschebor
Subjects: Numerical Analysis
AbstractWe 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.A numerical algorithm for zero counting II: Randomization and Condition.
Ср, 09/23/2009 - 13:19 — SomNambulAuthors: Felipe Cucker, Teresa Krick, Gregorio Malajovich, Mario Wschebor
Subjects: Numerical Analysis
AbstractThis paper was witdrawn by the authors.
A numerical algorithm for zero counting II: Randomization and Condition.
Ср, 09/23/2009 - 13:19 — SomNambulAuthors: Felipe Cucker, Teresa Krick, Gregorio Malajovich, Mario Wschebor
Subjects: Numerical Analysis
AbstractThis paper was witdrawn by the authors.
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