Stochastic Vs Worst-case Condition Numbers

Details Stochastic Vs Worst-case Condition Numbers Stochastic Vs Worst-case Condition Numbers

2008-12-18

arxiv.org/abs/0812.3613v2

Mathematics

Numerical Analysis

Scientific paper

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.

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