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/lp/de-gruyter/tikhonov-regularization-of-nonlinear-ill-posed-equations-under-general-9z4zJAi6ng
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- Publisher
- de Gruyter
- Copyright
- © de Gruyter
- ISSN
- 0928-0219
- eISSN
- 1569-3945
- DOI
- 10.1515/jiip.2007.044
- Publisher site
- See Article on Publisher Site
Abstract
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.
Journal
Journal of Inverse and Ill-Posed Problems – de Gruyter
Published: Dec 15, 2007
Keywords: Nonlinear ill-posed equations; Tikhonov regularization; source conditions; discrepancy principle; parameter choices