Vasin, V.George, S.2026-02-052014Applied Mathematics and Computation, 2014, 230, , pp. 406-413963003https://doi.org/10.1016/j.amc.2013.12.104https://idr.nitk.ac.in/handle/123456789/26525In this paper we consider the Lavrentiev regularization method and a modified Newton method for obtaining stable approximate solution to nonlinear ill-posed operator equations F(x)=y where F:D(F)?X?X is a nonlinear monotone operator or F?(x0) is nonnegative selfadjoint operator defined on a real Hilbert space X. We assume that only a noisy data y??X with ?y- y???? are available. Further we assume that Fréchet derivative F? of F satisfies center-type Lipschitz condition. A priori choice of regularization parameter is presented. We proved that under a general source condition on x0-x?, the error ?x?-xn,??? between the regularized approximation xn,??(x0,??;=x0) and the solution x? is of optimal order. In the concluding section the algorithm is applied to numerical solution of the inverse gravimetry problem. © 2013 Elsevier Inc. All rights reserved.Ill posed problemIll-posed operator equationInverse gravimetry problemLavrentiev regularizationsLipschitz conditionsNonlinear ill-posed problemsNonlinear monotone operatorRegularized approximationEuler equationsGravimetersMathematical operatorsNewton-Raphson methodInverse problems