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.
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| Author details: | Pornsarp Pornsawad, Nantawan Sapsakul, Christine BöckmannORCiD |
|---|---|
| URN: | urn:nbn:de:kobv:517-opus4-473433 |
| DOI: | https://doi.org/10.25932/publishup-47343 |
| ISSN: | 1866-8372 |
| Title of parent work (German): | Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe |
| Publication series (Volume number): | Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (1335) |
| Publication type: | Postprint |
| Language: | English |
| Date of first publication: | 2019/05/10 |
| Publication year: | 2019 |
| Publishing institution: | Universität Potsdam |
| Release date: | 2023/07/14 |
| Tag: | asymptotic method; discrepancy principle; nonlinear operator; optimal rate; regularization |
| Issue: | 1335 |
| Number of pages: | 19 |
| Source: | Mathematics 7 (2019) 419 DOI:10.3390/math7050419 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access / Green Open-Access |
| License (German): |  CC-BY - Namensnennung 4.0 International |
| External remark: | Bibliographieeintrag der Originalveröffentlichung/Quelle |
