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Abstract.
For solving a linear ill-posed problem, a combination of Tikhonov regularization and a finite dimensional projection method is considered. In the present paper we treat the dimension of the projection as the second parameter of regularization. The method using the discrepancy set of all regularization parameter pairs which satisfy a certain discrepancy principle is investigated. For the case of truncated SVD and LSQ projection methods, under the standard source conditions, an order of convergence is derived. This order of convergence is optimal under the same conditions as those for Tikhonov regularization with the discrepancy principle and without additional discretization.
Keywords: Ill-posed problems; least squares projection method; Tikhonov regularization; two-parameter regularization; discrepancy principle; order optimal error bound
Received: 2012-11-22
Published Online: 2013-08-01
Published in Print: 2013-08-01
© 2013 by Walter de Gruyter Berlin Boston
