A modified Newton-Lavrentiev regularization for nonlinear ill-posed Hammerstein-type operator equations

Recently, a new iterative method, called Newton-Lavrentiev regularization (NLR) method, was considered by George (2006) for regularizing a nonlinear ill-posed Hammerstein-type operator equation in Hilbert spaces. In this paper we introduce a modified form of the NLR method and derive order optimal error bounds by choosing the regularization parameter according to the adaptive scheme considered by Pereverzev and Schock (2005). (C) 2007 Elsevier Inc. All rights reserved.