Regularizing algorithms for detecting discontinuities in ill-posed problems

Abstract

The problem of detecting singularities (discontinuities of the first kind) of a noisy function in L2 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 δ is proved for some classes of functions with isolated singularities. New upper bounds for the singularity separation threshold are obtained.