A modified asymptotical regularization of nonlinear ill-posed problems
- In this paper, we investigate the continuous version of modified iterative Runge–Kutta-type methods for nonlinear inverse ill-posed problems proposed in a previous work. The convergence analysis is proved under the tangential cone condition, a modified discrepancy principle, i.e., the stopping time T is a solution of ∥𝐹(𝑥𝛿(𝑇))−𝑦𝛿∥=𝜏𝛿+ for some 𝛿+>𝛿, and an appropriate source condition. We yield the optimal rate of convergence.
Author details: | Pornsarp PornsawadORCiDGND, Nantawan Sapsakul, Christine BöckmannORCiDGND |
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DOI: | https://doi.org/10.3390/math7050419 |
ISSN: | 2227-7390 |
Title of parent work (English): | Mathematics |
Publisher: | MDPI |
Place of publishing: | Basel, Schweiz |
Publication type: | Article |
Language: | English |
Date of first publication: | 2019/05/10 |
Publication year: | 2019 |
Release date: | 2023/07/14 |
Tag: | asymptotic method; discrepancy principle; nonlinear operator; optimal rate; regularization |
Volume: | 7 |
Article number: | 419 |
Print run: | 5 |
Number of pages: | 19 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Extern / Extern | |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |
Publishing method: | Open Access / Gold Open-Access |
License (German): | CC-BY - Namensnennung 4.0 International |
External remark: | Zweitveröffentlichung in der Schriftenreihe Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 1335 |