In this Chapter we consider methods for solving ill-posed problems under the condition that the a priori information is, in general, insufficient in order to single out a compact set of well-posedness. The main ideas in this Chapter have been expressed in , . We will consider the case when the operator is also given approximately, while the set of constraints of the problem is a closed convex set in a Hilbert space. The case when the operator is specified exactly and the case when constraints are absent (i.e. the set of constraints coincides with the whole space) are instances of the problem statement considered here.
KeywordsHilbert Space Discrepancy Principle Regularization Parameter Extremal Problem Regularization Method
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