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

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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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