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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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Modulus of continuity and conditional stability for linear regularization schemes

M. Schieck1

1Department of Mathematics, Chemnitz University of Technology, D-09107 Chemnitz, Germany. Email:

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 17, Issue 1, Pages 85–89, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2009.010, February 2009

Publication History

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

Abstract

This paper surveys the concept of conditional stability for linear ill-posed problems with error estimates based on the modulus of continuity. Combining the ideas of [Hofmann, Mathé, Schieck, J. Inv. Ill-Posed Problems 16: 569–587, 2008] and [Kabanikhin, Schieck, J. Inv. Ill-Posed Problems 16: 267–282, 2008] fundamental properties are formulated and convergence rates results for regularized solutions concerning linear regularization schemes are carried out.

Key words.: Linear ill-posed problems; modulus of continuity; conditional stability; general regularization methods; profile functions

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[1]
Xiangtuan Xiong, Liqin Zhu, and Ming Li
Mathematics and Computers in Simulation, 2011, Volume 82, Number 2, Page 332

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