A discrete algorithm for localizing the discontinuity lines of a function of two variables
- Authors: Ageev A.L.1, Antonova T.V.1
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Affiliations:
- Krasovskii Institute of Mathematics and Mechanics
- Issue: Vol 11, No 4 (2017)
- Pages: 463-471
- Section: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/212843
- DOI: https://doi.org/10.1134/S1990478917040019
- ID: 212843
Cite item
Abstract
We consider an ill-posed problem of localizing the discontinuity lines of a function of two variables. It is assumed that, instead of a precisely given function f, the values are available of the averages on the square of the perturbed function fδ at the points of a uniform grid as well as the error level δ so that \({\left\| {f - {f^\delta }} \right\|_{{L_2}}}{(_\mathbb{R}}^2)\) ≤ δ. An algorithm is constructed for localizing the discontinuity lines, its convergence is proved with the estimates of the approximation accuracy, which coincide in the order of magnitude with the estimates obtained earlier by the authors for the case when, instead of the average values of the function fδ, the function itself is given. Also, we substantiate the estimates for an important characteristic of localization methods, i.e. separability threshold.
About the authors
A. L. Ageev
Krasovskii Institute of Mathematics and Mechanics
Author for correspondence.
Email: ageev@imm.uran.ru
Russian Federation, ul. S. Kovalevskoi 16, Ekaterinburg, 620990
T. V. Antonova
Krasovskii Institute of Mathematics and Mechanics
Email: ageev@imm.uran.ru
Russian Federation, ul. S. Kovalevskoi 16, Ekaterinburg, 620990