Abstract:
A function of two variables with the lines of discontinuity of the first kind is considered. It is assumed
that outside discontinuity lines the function to be measured is smooth and has a limited partial derivative.
Instead of the accurate function its approximation in $L_2$ and perturbation level are known. The problem in
question belongs to the class of nonlinear ill-posed problems, for whose solution it is required to construct
regularizing algorithms. We propose a reduced theoretical approach to solving the problem of localizing the
discontinuity lines of the function that is noisy in the space $L_2$. This is done in the case when conditions of
an exact function are imposed “in the small”. Methods of averaging have been constructed, the estimations of
localizing the line (in the small) have been obtained.
Key words:ill-posed problems, localization of singularities, line of discontinuity, regularization.
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