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Regularizing algorithms for detecting discontinuities in ill-posed problems. (Russian, English) Zbl 1199.47064
Zh. Vychisl. Mat. Mat. Fiz. 48, No. 8, 1362-1370 (2008); translation in Comput. Math. Math. Phys. 48, No. 8, 1284-1292 (2008).
Summary: 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.

MSC:
47A52 Linear operators and ill-posed problems, regularization
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