On the power of adaptive information for functions with singularities

Wasilkowski, G. W.; Gao, F.

doi:10.1090/S0025-5718-1992-1106987-X

On the power of adaptive information for functions with singularities
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by G. W. Wasilkowski and F. Gao PDF

Math. Comp. 58 (1992), 285-304 Request permission

Abstract:

We study from a probabilistic viewpoint the problem of locating singularities of functions using function evaluations. We show that, under the assumption of a Wiener-like probability distribution on the class of singular functions, an adaptive algorithm can locate a singular point accurately with only a small probability of failure. As an application, we show that an integration algorithm that adaptively locates a singular point is probabilistically superior to nonadaptive algorithms.

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