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On numerical realization of quasioptimal parameter choices in (iterated) Tikhonov and Lavrentiev regularization

    Toomas Raus Affiliation
    ; Uno Hämarik Affiliation

Abstract

We consider linear ill‐posed problems in Hilbert spaces with noisy right hand side and given noise level. For approximation of the solution the Tikhonov method or the iterated variant of this method may be used. In self‐adjoint problems the Lavrentiev method or its iterated variant are used. For a posteriori choice of the regularization parameter often quasioptimal rules are used which require computing of additionally iterated approximations. In this paper we propose for parameter choice alternative numerical schemes, using instead of additional iterations linear combinations of approximations with different parameters.


First published online: 14 Oct 2010

Keyword : ill‐posed problem, regularization, (iterated) Tikhonov method, (iterated) Lavrentiev method, quasioptimal rules, parameter choice, numerical schemes

How to Cite
Raus, T., & Hämarik, U. (2009). On numerical realization of quasioptimal parameter choices in (iterated) Tikhonov and Lavrentiev regularization. Mathematical Modelling and Analysis, 14(1), 99-108. https://doi.org/10.3846/1392-6292.2009.14.99-108
Published in Issue
Mar 31, 2009
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