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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 22, Issue 5


Locally extra-optimal regularizing algorithms

Alexander S. Leonov
  • Department of Mathematics, National Nuclear Research University `MEPHI', Kashirskoe Shosse 31, 115409 Moscow, Russia
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Published Online: 2013-12-07 | DOI: https://doi.org/10.1515/jip-2013-0056


So-called local a posteriori accuracy estimates for approximate solutions of ill-posed inverse problems are under investigation. We present an approach to local a posteriori estimation along with the numerical algorithm for calculating the estimators. We analyze the local optimality in order of obtained a posteriori accuracy estimates and introduce a new important notion of locally extra-optimal regularizing algorithm as a method for the solution of ill-posed problems having optimal in order local a posteriori accuracy estimates. Finally, we demonstrate the results of numerical experiments on applications of locally extra-optimal regularizing methods, constructed on the base of Tikhonov regularization, for calculating local a posteriori accuracy estimates.

Keywords: Ill-posed inverse problem; local a posteriori accuracy estimation; locally extra-optimal regularizing algorithm

MSC: 47A52; 47J06; 65N20

About the article

Received: 2013-09-17

Published Online: 2013-12-07

Published in Print: 2014-10-01

Funding Source: Russian Foundation for Basic Research

Award identifier / Grant number: 11-01-00040-a

Funding Source: Russian Foundation for Basic Research

Award identifier / Grant number: 12-01-91153-GFEN-a

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 22, Issue 5, Pages 713–737, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jip-2013-0056.

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