Stochastic Vs Worst-case Condition Numbers
Provides theoretical bounds for practitioners needing to understand the gap between average-case and worst-case numerical stability.
The paper compares stochastic and worst-case condition numbers for general computational problems, proving that the ratio of worst-case to stochastic condition number is O(√m) and the difference in loss of precision is O(ln m).
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.