TITLE

ON THE ANALOG OF THE MONOTONE ERROR RULE FOR PARAMETER CHOICE IN THE (ITERATED) LAVRENTIEV REGULARIZATION

AUTHOR(S)
Hämarik, U.; Raus, T.; Palm, R.
PUB. DATE
July 2008
SOURCE
Computational Methods in Applied Mathematics;2008, Vol. 8 Issue 3, p237
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We consider linear ill-posed problems in Hilbert spaces with a noisy right hand side and a given noise level. To solve non-self-adjoint problems by the (iterated) Tikhonov method, one effective rule for choosing the regularization parameter is the monotone error rule (Tautenhahn&Hämarik, Inverse Problems, 1999, 15, 1487-1505). In this paper we consider the solution of self-adjoint problems by the (iterated) Lavrentiev method and propose for parameter choice an analog of the monotone error rule. We prove under certain mild assumptions the quasi-optimality of the proposed rule guaranteeing convergence and order optimal error estimates. Numerical examples show for the proposed rule and its modifications much better performance than for the modified discrepancy principle.
ACCESSION #
34999304

 

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