New rule for choice of the regularization parameter in (iterated) tikhonov method
| Autor: | Toomas Raus, Uno Hämarik |
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| Jazyk: | angličtina |
| Rok vydání: | 2009 |
| Předmět: | |
| Zdroj: | Mathematical Modelling and Analysis, Vol 14, Iss 2 (2009) |
| Druh dokumentu: | article |
| ISSN: | 1392-6292 1648-3510 |
| DOI: | 10.3846/1392-6292.2009.14.187-198 |
| Popis: | We propose a new a posteriori rule for choosing the regularization parameter α in (iterated) Tikhonov method for solving linear ill‐posed problems in Hilbert spaces. We assume that data are noisy but noise level δ is given. We prove that (iterated) Tikhonov approximation with proposed choice of α converges to the solution as δ → 0 and has order optimal error estimates. Under certain mild assumption the quasioptimality of proposed rule is also proved. Numerical examples show the advantage of the new rule over the monotone error rule, especially in case of rough δ. First published online: 14 Oct 2010 |
| Databáze: | Directory of Open Access Journals |
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