Faculty Publications
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Item Expanding the applicability of a Newton-Lavrentiev regularization method for ill-posed problems(Publishing House of the Romanian Academy Calea 13 Septembrie nr. 13, Sector 5, 050711. P.O. Box 5-42, Bucuresti, 2013) Argyros, I.K.; George, S.We present a semilocal convergence analysis for a simplified Newton-Lavrentiev regularization method for solving ill-posed problems in a Hilbert space setting. We use a center-Lipschitz instead of a Lipschitz condition in our conver-gence analysis. This way we obtain: weaker convergence criteria, tighter error bounds and more precise information on the location of the solution than in earlier studies (such as [13]).Item Extended convergence of gauss-newton’s method and uniqueness of the solution(SINUS Association Office_CJEES@yahoo.ro, 2018) Argyros, I.K.; Cho, Y.J.; George, S.The aim of this paper is to extend the applicability of the Gauss-Newton’s method for solving nonlinear least squares problems using our new idea of restricted convergence domains. The new technique uses tighter Lipschitz functions than in earlier papers leading to a tighter ball convergence analysis. © 2018, SINUS Association. All rights reserved.Item On the solution of equations by extended discretization(MDPI Multidisciplinary Digital Publishing Institute rasetti@mdpi.com, 2020) Argyros, G.I.; Argyros, M.I.; Regmi, S.; Argyros, I.K.; George, S.The method of discretization is used to solve nonlinear equations involving Banach space valued operators using Lipschitz or Hölder constants. But these constants cannot always be found. That is why we present results using ?- continuity conditions on the Fréchet derivative of the operator involved. This way, we extend the applicability of the discretization technique. It turns out that if we specialize ?- continuity our new results improve those in the literature too in the case of Lipschitz or Hölder continuity. Our analysis includes tighter upper error bounds on the distances involved. © 2020 by the authors.Item Extending the applicability of newton’s algorithm with projections for solving generalized equations(MDPI AG diversity@mdpi.com, 2020) Argyros, M.I.; Argyros, G.I.; Argyros, I.K.; Regmi, S.; George, S.A new technique is developed to extend the convergence ball of Newton’s algorithm with projections for solving generalized equations with constraints on the multidimensional Euclidean space. This goal is achieved by locating a more precise region than in earlier studies containing the solution on which the Lipschitz constants are smaller than the ones used in previous studies. These advances are obtained without additional conditions. This technique can be used to extend the usage of other iterative algorithms. Numerical experiments are used to demonstrate the superiority of the new results. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.Item Expanding the applicability of Newton's method and of a robust modified Newton's method(Institute of Mathematics. Polish Academy of Sciences, 2021) Argyros, I.K.; George, S.Newton's method cannot be used to approximate a solution of a nonlinear equation when the derivative of the function is singular or almost singular. To overcome this problem a modified Newton's method may be used. The Newton-Kantorovich theorem is used to show its convergence. The convergence domain of this method is small in general. In the present study, we show how to expand the convergence domain of Newton's method and the modified Newton's method by using the center Lipschitz condition and more precise convergence domains than in earlier studies. Numerical examples are also presented. © Instytut Matematyczny PAN, 2021.