A Numerical Algorithm for Zero Counting. III: Randomization and Condition
Numerical Analysis
2012-05-31 v2 Probability
Abstract
In 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)).
Cite
@article{arxiv.1007.1597,
title = {A Numerical Algorithm for Zero Counting. III: Randomization and Condition},
author = {Felipe Cucker and Teresa Krick and Gregorio Malajovich and Mario Wschebor},
journal= {arXiv preprint arXiv:1007.1597},
year = {2012}
}