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New rule for choice of the regularization parameter in (iterated) tikhonov method

    Toomas Raus Affiliation
    ; Uno Hämarik Affiliation

Abstract

We propose a new a posteriori rule for choosing the regularization parameter α in (iterated) Tikhonov method for solving linear ill‐posed problems in Hilbert spaces. We assume that data are noisy but noise level δ is given. We prove that (iterated) Tikhonov approximation with proposed choice of α converges to the solution as δ → 0 and has order optimal error estimates. Under certain mild assumption the quasioptimality of proposed rule is also proved. Numerical examples show the advantage of the new rule over the monotone error rule, especially in case of rough δ.


First published online: 14 Oct 2010

Keyword : ill‐posed problem, (iterated) Tikhonov method, regularization parameter, a posteriori rule, monotone error rule, convergence, order optimality

How to Cite
Raus, T., & Hämarik, U. (2009). New rule for choice of the regularization parameter in (iterated) tikhonov method. Mathematical Modelling and Analysis, 14(2), 187-198. https://doi.org/10.3846/1392-6292.2009.14.187-198
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Jun 30, 2009
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