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- W1970616506 abstract "Abstract We consider linear ill-posed problems in Hilbert spaces with a noisy right hand side and a given noise level. To solve non-self-adjoint problems by the (it-erated) Tikhonov method, one effective rule for choosing the regularization parameter is the monotone error rule (Tautenhahn and Hamarik, Inverse Problems, 1999, 15, 1487– 1505). In this paper we consider the solution of self-adjoint problems by the (iterated) Lavrentiev method and propose for parameter choice an analog of the monotone error rule. We prove under certain mild assumptions the quasi-optimality of the proposed rule guaranteeing convergence and order optimal error estimates. Numerical examples show for the proposed rule and its modifications much better performance than for the modified discrepancy principle." @default.
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- W1970616506 date "2008-01-01" @default.
- W1970616506 modified "2023-10-14" @default.
- W1970616506 title "On The Analog Of The Monotone Error Rule For Parameter Choice In The (Iterated) Lavrentiev Regularization" @default.
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- W1970616506 doi "https://doi.org/10.2478/cmam-2008-0017" @default.
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