Stochastic Vs Worst-case Condition Numbers
Numerical Analysis
2008-12-25 v2
Abstract
We compare Stochastic and Worst-case condition numbers and loss of precision for general computational problems. We show an upper bound for the ratio of Worst-case condition number to the Stochastic condition number of order O(sqrt m). We show an upper bound for the difference between the Worst-case loss of precision and the Stochastic loss of precision of order O(ln m). The results hold if the perturbations are measured norm-wise or componentwise.
Cite
@article{arxiv.0812.3613,
title = {Stochastic Vs Worst-case Condition Numbers},
author = {Dennis Cheung and Lisa H. Y. Zhou},
journal= {arXiv preprint arXiv:0812.3613},
year = {2008}
}