Multi-Parameter Tikhonov Regularization for Linear Ill-Posed Operator Equations

Multi-Parameter Tikhonov Regularization for Linear Ill-Posed Operator Equations

Year:    2008

Journal of Computational Mathematics, Vol. 26 (2008), Iss. 1 : pp. 37–55

Abstract

We consider solving linear ill-posed operator equations. Based on a multi-scale decomposition for the solution space, we propose a multi-parameter regularization for solving the equations. We establish weak and strong convergence theorems for the multi-parameter regularization solution. In particular, based on the eigenfunction decomposition, we develop a posteriori choice strategy for multi-parameters which gives a regularization solution with the optimal error bound. Several practical choices of multi-parameters are proposed. We also present numerical experiments to demonstrate the outperformance of the multi-parameter regularization over the single parameter regularization.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2008-JCM-8609

Journal of Computational Mathematics, Vol. 26 (2008), Iss. 1 : pp. 37–55

Published online:    2008-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Ill-posed problems Tikhonov regularization Multi-parameter regularization.