Davide Bianchi,
Marco Donatelli
S. 73 - 99
doi:
10.1553/etna_vol47s73
doi:
10.1553/etna_vol47s73
Abstract:
We investigate the recently introduced Tikhonov regularization filters with penalty terms having seminorms that depend on the operator itself. Exploiting the singular value decomposition of the operator, we provide optimal order conditions, smoothing properties, and a general condition (with a minor condition of the seminorm) for the saturation level. Moreover, we introduce and analyze both stationary and nonstationary iterative counterparts of the generalized Tikhonov method with operator-dependent seminorms. We establish their convergence rate under conditions affecting only the iteration parameters, proving that they overcome the saturation result. Finally, some selected numerical results confirm the effectiveness of the proposed regularization filters.
ill-posed problems, fractional Tikhonov regularization, iterated Tikhonov, filter functions
Published Online:
2017/11/15 12:55:32
Object Identifier:
0xc1aa5576 0x00371068
Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.
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