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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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Regularization in Banach spaces — convergence rates by approximative source conditions

T. Hein1

1Technische Universität Chemnitz, Fakultät für Mathematik, D-09107 Chemnitz, Deutschland. Email:

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 17, Issue 1, Pages 27–41, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2009.004, February 2009

Publication History

Received:
2008-07-25
Published Online:
2009-02-04

Abstract

In this paper we deal with convergence rates for a Tikhonov regularization approach for linear and nonlinear ill-posed problems in Banach spaces. Here, we deal with so-called distance functions which quantify the violation of a given reference source condition. With the aid of these functions we present error bounds and convergence rates for regularized solutions of linear and nonlinear problems when the reference source condition is violated. Introducing this topic for linear problems we extend the theory also to nonlinear problems. Finally an a-posteriori choice of the regularization parameter is suggested yielding the optimal convergence rate.

Key words.: Ill-posed problem; regularization; Banach space; distance function; convergence rates

Citing Articles

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[1]
T. Hein
Mathematical Modelling and Analysis, 2009, Volume 14, Number 4, Page 451
[2]
Torsten Hein and Kamil S. Kazimierski
Numerical Functional Analysis and Optimization, 2010, Volume 31, Number 10, Page 1158

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