George, S.2026-02-052010Journal of Inverse and Ill-Posed Problems, 2010, 18, 2, pp. 133-1469280219https://doi.org/10.1515/JIIP.2010.004https://idr.nitk.ac.in/handle/123456789/27539In this paper we consider regularized modified Newton's method for approximately solving the nonlinear ill-posed problem F(x) = y, where the right hand side is replaced by noisy data y?? Y with y - y?? ? and F : D(F) ? X ? Y is a nonlinear operator between Hilbert spaces X and Y. Under the assumption that Fréchet derivative F? of F is Lipschitz continuous, a choice of the regularization parameter and a stopping rule based on a majorizing sequence are presented. We prove that under a general source condition on , the error between the regularized approximation and the solution of optimal order. © de Gruyter 2010.Euler equationsMathematical operatorsNumerical methodsTungsten compoundsLipschitz continuousMajorizing sequencesModified Newton's methodNonlinear ill-posed problemsRegularization parametersRegularized approximationRegularized newton's methodsTihkonov regularizationNewton-Raphson method