This article is cited in 25 papers

A posteriori accuracy estimations of solutions of ill-posed inverse problems and extra-optimal regularizing algorithms for their solution

A. S. Leonov

Moscow Engineering Physics Institute (State University), Moscow

Abstract: A new scheme of a posteriori accuracy estimation for approximate solutions of ill-posed inverse problems is presented along with an algorithm of calculating this estimation. A new notion of extra-optimal regularizing algorithm is introduced as a method for solving ill-posed inverse problems having optimal in order a posteriori accuracy estimation. Sufficient conditions of extra-optimality are formulated and an example of extra-optimal regularizing algorithm is given. The developed theory is illustrated by numerical experiments.

Key words: ill-posed problems, regularizing algorithms, a posteriori accuracy estimation, extra-optimal algorithm.

UDC: 517.977

Received: 15.02.2011

 English version: Numerical Analysis and Applications, 2012, 5:1, 68–83

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