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April 27, 2026Journal of Inverse and Ill-Posed Problems0 citations

A posteriori error estimates in linear ill-posed problems

ALA. S. LeonovNational Research Nuclear University MEPhI

Key Points

This research aims to investigate a posteriori error estimates for approximate solutions in linear ill-posed inverse problems.
Overview of existing error estimation approaches in linear ill-posed problems.
Studied variational a posteriori error estimates in various function spaces.
Developed a solution algorithm for the canonical problem, demonstrating faster performance than previous methods.
Introduced a solution algorithm that operates significantly faster than previous algorithms.
Provided error estimates applicable to various Hilbert and Banach spaces.
Illustrated the approach using a two-dimensional heat conduction model inverse problem.

Abstract

Abstract A posteriori error estimates for approximate solutions of linear ill-posed inverse problems are under investigation. A brief overview of existing approaches to this problem is given. Special variational a posteriori error estimates are studied for various classes of function spaces. Obtaining all such estimates reduces to solving a certain canonical problem. For the canonical problem, a solution algorithm is given in various forms. This algorithm is several times faster than previously proposed ones. The estimates and algorithm are suitable for various Hilbert and Banach spaces. The obtaining of such estimates is illustrated using the example of a two-dimensional model inverse problem of heat conduction.

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