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Mathematics of Computation

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On the power of adaptive information for functions with singularities

Authors: G. W. Wasilkowski and F. Gao
Journal: Math. Comp. 58 (1992), 285-304
MSC: Primary 65D15; Secondary 62L12, 65D30
MathSciNet review: 1106987
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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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Keywords: Piecewise regular functions, approximating/detecting singular points, probabilistic analysis of algorithms, adaptive (sequential) algorithms, adaptive quadratures
Article copyright: © Copyright 1992 American Mathematical Society