Pade iteration method for regularization
- In this study we present iterative regularization methods using rational approximations, in particular, Pade approximants, which work well for ill-posed problems. We prove that the (k,j)-Pade method is a convergent and order optimal iterative regularization method in using the discrepancy principle of Morozov. Furthermore, we present a hybrid Pade method, compare it with other well-known methods and found that it is faster than the Landweber method. It is worth mentioning that this study is a completion of the paper [A. Kirsche, C. Bockmann, Rational approximations for ill-conditioned equation systems, Appl. Math. Comput. 171 (2005) 385-397] where this method was treated to solve ill-conditioned equation systems. (c) 2006 Elsevier Inc. All rights reserved.
| Author details: | Andreas KirscheGND, Christine BöckmannORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1016/j.amc.2006.01.011 |
| ISSN: | 0096-3003 |
| Title of parent work (English): | Applied mathematics and computation |
| Publisher: | Elsevier |
| Place of publishing: | New York |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2006/09/15 |
| Publication year: | 2006 |
| Release date: | 2020/05/26 |
| Tag: | Pade approximants; ill-posed problem; iterative regularization |
| Volume: | 180 |
| Issue: | 2 |
| Number of pages: | 16 |
| First page: | 648 |
| Last Page: | 663 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
