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A Quadratic Convergence Yielding Iterative Method for Nonlinear Ill-posed Operator Equations

Santhosh George and Atef Ibrahim Elmahdy

Abstract

In this paper, we consider an iterative method for the approximate solution of the nonlinear ill-posed operator equation Tx = y. The iteration procedure converges quadratically to the unique solution of the equation for the regularized approximation. It is known that (Tautanhahn (2002)) this solution converges to the solution of the given ill-posed operator equation. The convergence analysis and the stopping rule are based on a suitably constructed majorizing sequence. We show that the adaptive scheme considered by Perverzev and Schock (2005) for choosing the regularization parameter can be effectively used here for obtaining an optimal order error estimate.

Received: 2010-07-22
Revised: 2010-12-13
Accepted: 2011-04-15
Published Online: 2012
Published in Print: 2012

© Institute of Mathematics, NAS of Belarus