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Hein, Torsten; Kazimierski, Kamil S. : Modified Landweber iteration in Banach spaces - convergence and convergence rates

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