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Publication Date:
January 2008
ISSN:
1569-3945
DOI:
10.1515/jiip.2007.044

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Editor-in-Chief: Kabanikhin, Sergey I.

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Tikhonov regularization of nonlinear ill-posed equations under general source condition

Pallavi Mahale1 / M. Thamban Nair2

1 Department of Mathematics, IIT Madras, Chennai-600036, India. Email: pallavimahale@iitm.ac.in

2 Department of Mathematics, IIT Madras, Chennai-600036, India. Email: mtnair@iitm.ac.in

Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 15, Issue 8, Pages 813–829, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/jiip.2007.044, January 2008

Publication History:
Received:
2006-12-15
Revised:
2007-06-19
Published Online:
2008-01-24

Tikhonov regularization is one of the widely used procedures for the regularization of nonlinear as well as linear ill-posed problems. The error analysis carried out in most of the works that appeared in last few years on Tikhonov regularization of nonlinear ill-posed problems are under Hölder type source conditions on the unknown solution which is known to be applicable only for mildly ill-posed problems. In this paper we consider Tikhonov regularization of nonlinear ill-posed problems and derive order optimal error estimate under a general source condition together with an a posteriori parameter rule proposed by Scherzer et al., which is applicable for severely ill-posed problems as well.

Keywords: Nonlinear ill-posed equations; Tikhonov regularization; source conditions; discrepancy principle; parameter choices

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