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Extrapolation of Tikhonov regularization method

    Uno Hämarik Affiliation
    ; Reimo Palm Affiliation
    ; Toomas Raus Affiliation

Abstract

We consider regularization of linear ill‐posed problem Au = f with noisy data fδ, ¦fδ - f¦≤ δ . The approximate solution is computed as the extrapolated Tikhonov approximation, which is a linear combination of n ≥ 2 Tikhonov approximations with different parameters. If the solution u* belongs to R((A*A) n ), then the maximal guaranteed accuracy of Tikhonov approximation is O(δ 2/3) versus accuracy O(δ 2n/(2n+1)) of corresponding extrapolated approximation. We propose several rules for choice of the regularization parameter, some of these are also good in case of moderate over‐ and underestimation of the noise level. Numerical examples are given.


First published online: 09 Jun 2011

Keyword : ill‐posed problems, regularization, Tikhonov method, extrapolation, noise level, regularization parameter choice, balancing principle, monotone error rule, rule R2

How to Cite
Hämarik, U., Palm, R., & Raus, T. (2010). Extrapolation of Tikhonov regularization method. Mathematical Modelling and Analysis, 15(1), 55-68. https://doi.org/10.3846/1392-6292.2010.15.55-68
Published in Issue
Feb 15, 2010
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