Morozov's Discrepancy Principle for the Tikhonov Regularization of Exponentially Ill-Posed Problems

Abstract

The problem of approximate solution of severely ill-posed problems given in the form of linear operator equations of the first kind with approximately known right-hand sides was considered. We have studied a strategy for solving this type of problems, which consists in combinating of Morozov's discrepancy principle and a finite-dimensional version of the Tikhonov regularization. It is shown that this combination provides an optimal order of accuracy on source sets. © 2008, Institute of Mathematics, NAS of Belarus. All rights reserved.