This article is cited in 13 papers

Regularizing algorithms for detecting discontinuities in ill-posed problems

A. L. Ageev, T. V. Antonova

Institute of Mathematics and Mechanics, Ural Division, Russian Academy of Sciences, ul. S. Kavalevskoi 16, Yekaterinburg, 620219, Russia

Abstract: The problem of detecting singularities (discontinuities of the first kind) of a noisy function in $L_2$ is considered. A wide class of regularizing algorithms that can detect discontinuities is constructed. New estimates of accuracy of determining the location of discontinuities are obtained and their optimality in terms of order with respect to the error level $\delta$ is proved for some classes of functions with isolated singularities. New upper bounds for the singularity separation threshold are obtained.

Key words: ill-posed problems, detection of discontinuities, regularizing algorithms, separation threshold.

UDC: 519.642.8

Received: 05.12.2006
Revised: 26.02.2007

 English version: Computational Mathematics and Mathematical Physics, 2008, 48:8, 1284–1292

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