Kaiserslautern - Fachbereich Mathematik
Refine
Year of publication
- 2003 (1) (remove)
Document Type
- Preprint (1) (remove)
Language
- English (1)
Has Fulltext
- yes (1) (remove)
Keywords
- Abel integral equations (1) (remove)
Faculty / Organisational entity
We study a possiblity to use the structure of the regularization error for a posteriori choice of the regularization parameter. As a result, a rather general form of a selection criterion is proposed, and its relation to the heuristical quasi-optimality principle of Tikhonov and Glasko (1964), and to an adaptation scheme proposed in a statistical context by Lepskii (1990), is discussed. The advantages of the proposed criterion are illustrated by using such examples as self-regularization of the trapezoidal rule for noisy Abel-type integral equations, Lavrentiev regularization for non-linear ill-posed problems and an inverse problem of the two-dimensional profile reconstruction.