Hein, Torsten ; Kazimierski, Kamil S. : Modified Landweber iteration in Banach spaces - convergence and convergence rates
- Author(s):
-
Hein, Torsten
Kazimierski, Kamil S.
- Title:
- Modified Landweber iteration in Banach spaces - convergence and convergence rates
- Electronic source:
-
application/pdf
- Preprint series:
- Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 14, 2009
- Mathematics Subject Classification:
-
47A52 [ Ill-posed problems, regularization ] 65F10 [ Iterative methods for linear systems ] 46E15 [ Banach spaces of continuous, differentiable or analytic functions ] 46B20 [ Geometry and structure of normed linear spaces ] - Abstract:
- We introduce and discuss an iterative method of relaxed Landweber type for the regularization of the solution operator of the operator equation $F(x)=y$, where $X$ and $Y$ are Banach spaces and $F$ is a non-linear, continuous operator mapping between them. We assume that the Banach space $X$ is smooth and convex of power type. We will show that under the so-called approximate source conditions convergence rates may be achieved. We will close our discussion with the presentation of a numerical example.
- Keywords:
- Iterative Regularization, Landweber iteration, Banach spaces, smooth of power type, convex of power type, Bregman distance
- Language:
-
English
- Publication time:
- 8 / 2009
