Optimal order of convergence for stable evaluation of differential operators

Abstract

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.

Keywords

• Regularization
• unbounded operator
• optimal convergence
• stable.