A General Framework for Regularized Evaluation of Unstable Operators*

A general approach is developed for stable evaluation of unbounded operators when the data are corrupted by error. The essence of the approach is to recast the direct problem of evaluating the unstable operator as an inverse problem involving an associated bounded operator. Classical general regularization methods for inverse problems are then elucidated within the new setting, and new order optimal parameter choice strategies for iterative and noniterative regularization methods are developed. Finally, a regularizing stopping rule for a conjugate gradient acceleration of Lardy’s method is provided.