On the Adaptive Selection of the Parameter in Regularization of Ill-Posed Problems
نویسندگان
چکیده
We study a possibility to use the structure of the regularization error for a posteriori choice of the regulatization 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 propsed in a statistical context by Lepskii (1990), is discussed. The advantages of the proposed criterion are illustrated by using such examples as selfregulatization 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.
منابع مشابه
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عنوان ژورنال:
- SIAM J. Numerical Analysis
دوره 43 شماره
صفحات -
تاریخ انتشار 2005