The discretized discrepancy principle under general source conditions

Authors:
Peter Mathé;Sergei V. Pereverzev
Affiliations:
Weierstraß Institute for Applied Analysis and Stochastics, Mohrenstraße 39, D-10117 Berlin, Germany;Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstraße 69, A-4040 Linz, Austria
Venue:
Journal of Complexity
Year:
2006

Citing 2
Cited 0

A posteriori parameter choice for general regularization methods for solving linear ill-posed problems

Applied Numerical Mathematics
A Technique for the Numerical Solution of Certain Integral Equations of the First Kind

Journal of the ACM (JACM)

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Abstract

We discuss adaptive strategies for choosing regularization parameters in Tikhonov-Phillips regularization of discretized linear operator equations. Two rules turn out to be based entirely on data from the underlying regularization scheme. Among them, only the discrepancy principle allows us to search for the optimal regularization parameter from the easiest problem. This potential advantage cannot be achieved by the standard projection scheme. We present a modified scheme, in which the discretization level varies with the successive regularization parameters, which has the advantage, mentioned before.