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Fast multilevel iteration methods for solving nonlinear ill-posed problems

  • Suhua Yang , Xingjun Luo EMAIL logo und Rong Zhang
Veröffentlicht/Copyright: 3. Mai 2023

Abstract

We propose a multilevel iteration method for the numerical solution of nonlinear ill-posed problems in the Hilbert space by using the Tikhonov regularization method. This leads to fast solutions of the discrete regularization methods for the nonlinear ill-posed equations. An adaptive choice of an a posteriori rule is suggested to choose the stopping index of iteration, and the rates of convergence are also derived. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed method.

MSC 2020: 65J20; 65R20

Funding statement: Supported in part by the Natural Science Foundation of China under grants 12201126, 11761010 and 62266002.

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Received: 2022-07-18
Revised: 2023-02-21
Accepted: 2023-03-11
Published Online: 2023-05-03
Published in Print: 2023-10-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 28.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/jiip-2022-0059/html
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