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Statistical Condition Estimation in Numerical Linear Algebra
Applied Math| Speaker: | Alan Laub, Dept. of Computer Science & Dept. of Applied Science, UC Davis |
| Location: | 693 Kerr |
| Start time: | Fri, Oct 12 2001, 4:10PM |
A statistically-based condition estimation procedure for general matrix functions is presented. Computational sensitivity is estimated by measuring the effect of random perturbations at the point of evaluation. In this procedure the (small) number of extra function evaluations used to evaluate the condition estimate determines the order of the estimate. That is, the probability that the estimate is off by a given factor is inversely proportional to the factor raised to the order of the method. The "transpose-free'' nature of the method allows it to be applied to a broad range of problems in which the function maps between spaces of different dimensions. Several examples illustrate the flexibility of the new estimation procedure in handling a variety of problems and types of sensitivity estimates, such as mixed and componentwise condition estimates in numerical linear algebra.
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