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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 |
Description
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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