This article is cited in 1 paper

Investigation of methods of localization of $q$-jumps and discontinities of firsth king of noisy function

A. L. Ageev, T. V. Antonova

Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya str., Ekaterinburg, 620990 Russia

Abstract: We consider the problem of localizing (determination of position) of discontinuities of the first kind of a function of one variable and the problem of localizing $q$-jumps of a noisy function. In the first case it is assumed that the exact function is smooth except for a finite number of discontinuities of the first kind. In the second case, the exact function is smooth except for a finite number of small segments of length $2q$. It is required that the number of discontinuities ($q$-jumps) be determined and approximated their position from an approximately given function and the level of the perturbation in $L_2(\mathbb{R})$. We construct a class of regular averaging methods and obtain and estimates of the accuracy of localization, separability, and observability on classes of correctness.

Keywords: ill-posed problems, regularizing method, separation threshold, threshold of observability, discontinuity of the first kind, $q$-jump.

UDC: 517.988

Received: 28.05.2018
Revised: 18.07.2018
Accepted: 26.09.2018

DOI: 10.26907/0021-3446-2019-7-3-14

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2019, 63:7, 1–11

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