The Optimal Order of Convergence for Stable Evaluation of Differential Operators
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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.