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.

Published
May 27, 2017
How to Cite
ARGYROS, Ioannis K.; GEORGE, Santhosh; JIDESH, P. Iterative regularization for ill-posed operator equations in Hilbert scales. Nonlinear Studies, [S.l.], v. 24, n. 2, p. 257-261, may 2017. ISSN 2153-4373. Available at: <http://nonlinearstudies.com/index.php/nonlinear/article/view/956>. Date accessed: 15 dec. 2017.