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Brief communications

Localization of discontinuities of the first kind methods for the solution of a convolution-type equation

D. V. Kurlikovskii

Chair of Computational Mathematics, Institute of Mathematics and Computer Sciences, Ural Federal University named after the first President of Russia B. N. Yeltsin, 4 Turgeneva str., Ekaterinburg, 620075 Russia

Abstract: We consider a convolution-type equation of the first kind from $L_1$ to $L_1$. We construct and investigate regularizing methods for localization (detection of positions) of discontinuities of the first kind of solution to this equation. Under additional conditions of exact solution, we obtain estimates for the accuracy of localization and for the separability threshold, which are another important characteristics of the methods.

Keywords: ill-posed problem, localization of singularities, regularizing method, separation threshold.

UDC: 517.988

Presented by the member of Editorial Board: V. V. Vasin
Received: 18.09.2013

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2014, 58:3, 60–63

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