George, S.Pareth, S.Kunhanandan, M.2026-02-052013Applied Mathematics and Computation, 2013, 219, 24, pp. 11191-11197963003https://doi.org/10.1016/j.amc.2013.05.021https://idr.nitk.ac.in/handle/123456789/26760In this paper we consider the two step method for approximately solving the 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, in the setting of Hilbert scales. We derive the error estimates by selecting the regularization parameter ? according to the adaptive method considered by Pereverzev and Schock in (2005), when the available data is f? with ?-f-f??- ??. The error estimate obtained in the setting of Hilbert scales { <inf>Xr}r?R</inf> generated by a densely defined, linear, unbounded, strictly positive self adjoint operator L:D(L)X?X is of optimal order. © 2013 Elsevier Inc. All rights reserved.Adaptive methodsHilbert scaleIll posed problemLavrentiev regularizationsMonotone operatorsNewton-Raphson methodMathematical operators