ON THE SEMILOCAL CONVERGENCE OF MODIFIED NEWTON-TIKHONOV REGULARIZATION METHOD FOR NONLINEAR ILL-POSED PROBLEMS

Santhosh George, Ioannis K. Argyros

Abstract


In this study, we introduce a new modified Newton-Tikhonov method for ap-proximating a solution of nonlinear ill-posed problems. The proposed iteration convergesquadratically. Order optimal error bounds are given in case the regularization parameter ischosen a priori and by the adaptive method of Pereverzev and Schock(2005).

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ISSN: 1229-1595 (Print), 2466-0973 (Online)