Abstract—A Two Step Newton-Tikhonov Projection method is presented for obtaining a stable approximate solution of nonlinear ill-posed Hammerstein type operator equations KF(x) =f. The regularization parameter is chosen according to the adaptive parameter choice strategy suggested by Perverzev and Schock (2005). The error estimates obtained with respect to the general source conditions are of optimal order. We also give the numerical example which confirms the efficiency of the proposed method.

Index Terms—Adaptive method, discretized newton tikhonov method, hammerstein operators, monotone operator, regularization.

Monnanda Erappa Shobha is with the Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal, India-575025 (e-mail: shobha.me@gmail.com).

Cite:Monnanda Erappa Shobha, "On Improving the Semi-Local Convergence of Newton-Type Projection Method for Ill-Posed Hammerstein Type Operator Equations," International Journal of Applied Physics and Mathematics vol. 3, no. 3, pp. 161-166, 2013.