George, S.Pareth, S.2020-03-312020-03-312013Journal of Applied Analysis, 2013, Vol.19, 2, pp.181-19610.1515/jaa-2013-0011https://idr.nitk.ac.in/handle/123456789/9860Motivated by the two-step directional Newton method considered by Argyros and Hilout (2010) for approximating a zero x* of a differentiable function F defined on a convex set D of a Hilbert space H, we consider a two-step Newton-Lavrentiev method (TSNLM) for obtaining an approximate solution to the nonlinear ill-posed operator equation F(x) = f , where F : D(F) ? X ? X is a nonlinear monotone operator defined on a real Hilbert space X. It is assumed that F(x) = f and that the only available data are f? with f - f? = ? ?. We prove that the TSNLM converges cubically to a solution of the equation F(x)+?(x-xo) = f? (such solution is an approximation of O x) where x0 is the initial guess. Under a general source condition on x0- x?, we derive order optimal error bounds by choosing the regularization parameter ? according to the balancing principle considered by Perverzev and Schock (2005). The computational results provided endorse the reliability and effectiveness of our method. 2013 by Walter de Gruyter Berlin Boston.Article