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