Electron.n. J. Diff. Eqns. Vol. 1993(1993), No. 04, pp. 1-10.

The Optimal Order of Convergence for Stable Evaluation of Differential Operators

C.W. Groetsch & O. Scherzer

Abstract:

An optimal order of convergence result, with respect to the error level in the data, is given for a Tikhonov-like method for approximating values of an unbounded operator. It is also shown that if the choice of parameter in the method is made by the discrepancy principle, then the order of convergence of the resulting method is suboptimal. Finally, a modified discrepancy principle leading to an optimal order of convergence is developed.

Submitted June 14, 1993. Published October 14, 1993.
Math Subject Classification: 47A58, 65J70.
Key Words: Regularization, unbounded operator, optimal convergence, stable.

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C.W. Groetsch
Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221-0025, USA
e-mail: groetsch@ucbeh.san.uc.edu

O. Scherzer
Institut fur Mathematik, Universitat Linz, A-4040 Linz, Austria
e-mail: scherzer@indmath.uni-linz.ac.at

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