Pallavi Mahale,
Ankit Singh
S. 450 - 469
doi:
10.1553/etna_vol58s450
Verlag der Österreichischen Akademie der Wissenschaften
doi:
10.1553/etna_vol58s450
Abstract:
In this paper, we consider the iterative Lavrentiev regularization method for obtaining a stable approximate solution for a nonlinear ill-posed operator equation $F(x)=y$, where $ F:D(F) \subset X \rightarrow X$ is a nonlinear monotone operator on the Hilbert spaces $X$. In order to obtain a stable approximate solution using iterative regularization methods, it is important to use a suitable stopping rule to terminate the iterations at the appropriate step. Recently, Qinian Jin and Wei Wang (2018) have proposed a heuristic rule to stop the iterations for the iteratively regularized Gauss-Newton method. The advantage of a heuristic rule over the existing a priori and a posteriori rules is that it does not require accurate information on the noise level, which may not be available or reliable in practical applications. In this paper, we propose a heuristic stopping rule for an iterated Lavrentiev regularization method.We derive error estimates under suitable nonlinearity conditions on the operator $F$.
Lavrentiev regularization, nonlinear ill-posed problems, heuristic parameter choice rules
Published Online:
2023/07/03 09:34:27
Object Identifier:
0xc1aa5572 0x003e59b2
Rights:All rights reserved.For questions regarding copyright and copies please contact us by email.
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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