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 Pornsawad, Nantawan Sapsakul, Christine BöckmannORCiD |
|---|---|
| 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 |
