An Information-Based Approach to III-Posed Problems

Arthur G. Werschulz
A problem is said to be ill-posed if the solution of the problem does not depend continuously on the input data. In this survey paper, we consider two different information-based settings for the optimal computation of approximate solution of ill-posed linear problems, namely the worst case and average case settings. These settings are studied for two different error criteria, namely, the absolute error and the residual error criteria. The main result for the absolute-error criterion...
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