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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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1569-3945
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Volume 16, Issue 3

Issues

Impact of conditional stability: Convergence rates for general linear regularization methods

S. I. Kabanikhin / M. Schieck
Published Online: 2008-05-26 | DOI: https://doi.org/10.1515/JIIP.2008.016

Abstract

The paper is devoted to the analysis of linear ill-posed operator equations Ax = y with an injective, compact linear forward operator A : XY mapping between Hilbert spaces X, Y. We are going to combine the ideas of [S. I. Kabanikhin, Convergence rate estimation of gradients methods via conditional stability of inverse and ill-posed problems. J. Inv. Ill-Posed Problems 13 (2005), 259–264.] and [S. I. Kabanikhin, Conditional stability stopping rule for gradient methods applied to inverse and ill-posed problems. J. Inv. Ill-Posed Problems 14 (2006), 805–812.] concerning the conditional stability on some subset MX and the ideas of [B. Hofmann and P. Mathé, Analysis of profile functions for general linear regularization methods. SIAM J. Numer. Anal. 45 (2007), 1122–1141.] concerning profile functions in order to find convergence rates for general linear regularization methods. Moreover, an extension to Lavrentiev regularization is given.

Key words.: Linear ill-posed problem; general linear regularization methods; conditional stability; profile function; source condition; convergence rates

About the article

S. I. Kabanikhin, Sobolev Institute of Mathematics, Koptyug prosp. 4, Novosibirsk 630090, Russia. Email:

M. Schieck, Department of Mathematics, Chemnitz University of Technology, 09107 Chemnitz, Germany. Email:


Published Online: 2008-05-26

Published in Print: 2008-05-01


Citation Information: Journal of Inverse and Ill-posed Problems, Volume 16, Issue 3, Pages 267–282, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/JIIP.2008.016.

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[2]
U. Tautenhahn, U. Hämarik, B. Hofmann, and Y. Shao
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T. Regińska and U. Tautenhahn
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B. Hofmann, P. Mathé, and M. Schieck
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