Electronic Journal of Differential Equations, Vol. 1993(1993), No. 04, pp. 1-10.

Title: Optimal rate of convergence for stable evaluation of 
       differential operators


Authors: C. W. Groetsch (Univ. of Cincinnati, OH, USA)
         O.  Scherzer (Univ. Linz, Linz, Austria)

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 a 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.