This article is cited in 4 papers

Effective algorithms for computing global and local posterior error estimates of solutions to linear ill-posed problems

A. S. Leonov

National Research Nuclear University MEPhY, 31 Kashirskoe Shosse, Moscow, 115409 Russia

Abstract: We consider the problems of calculating global and local a-posteriori error estimates of approximate solutions to ill-posed inverse problems, introduced and investigated earlier by the author. For linear inverse problems in Hilbert spaces, they consist in maximizing a quadratic functional with two quadratic constraints. The article shows how under certain conditions these problems can be reduced to a problem of maximizing a special (written analytically) differentiable functional with one constraint. New algorithms for calculating global and local a-posteriori error estimates based on the solution of these problems are proposed. Their effectiveness is illustrated by numerical experiments on a-posteriori error estimation of solutions to the model two-dimensional inverse problem of potential continuation. Experiments show that the proposed algorithms give a-posteriori error estimates close to the true error values. Proposed algorithms for global a-posteriori error estimation turn out to be more rapid (3 to 5 times) than the previously known algorithms.

Keywords: linear ill-posed problems, regularizing algorithms, a-posteriori error estimates.

UDC: 519.642

Received: 03.02.2019
Revised: 05.03.2019
Accepted: 27.03.2019

DOI: 10.26907/0021-3446-2020-2-29-38

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2020, 64:2, 26–34

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