Iterative regularization for ill-posed operator equations in Hilbert scales

  • Ioannis K. Argyros Cameron University
  • Santhosh George Karnakata Institute
  • P Jidesh

Abstract

In this paper we report on a method for regularizing a nonlinear ill-posed operator equation in Hilbert scales. The proposed  method is a combination of Lavrentiev regularization method and a Modified Newton's method in Hilbert scales . Under the assumptions that the operator F is continuously differentiable with a Lipschitz-continuous first derivative and that the solution of (\ref{eq:1}) fulfils a general source condition, we  give an optimal order convergence rate result with respect to the general source function.

Author Biographies

Ioannis K. Argyros, Cameron University
Professor Dr.Of Mathematics
Santhosh George, Karnakata Institute
Professor of Mathematics
Published
2017-05-27