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Hein, Torsten : Analytic and numerical comparison of linear direct and iterative regularization methods

Hein, Torsten : Analytic and numerical comparison of linear direct and iterative regularization methods

Author(s):
Hein, Torsten
Title:
Analytic and numerical comparison of linear direct and iterative regularization methods
Electronic source:
application/postscript
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 18, 2004
Mathematics Subject Classification:
65J20 [ Improperly posed problems; regularization ]
65D25 [ Numerical differentiation ]
65F20 [ Overdetermined systems, pseudoinverses ]
65R20 [ Integral equations ]
Abstract:
The paper deals with analytic and numerical studies of linear regularization methods. Thereby Tikhonov regularization and Landweber iteration are compared. In particular the regularization with semi-norms for both methods are considered. A heuristc approach for improving the results for Landweber iteration are introduced. The analytic considerations are illustrated by a detailed numerical study.
Keywords:
ill-posed linear problem, Moore-Penrose inverse, Tikhonov regularization, Landweber iteration, semi-norm, convergence rates, integral equation
Language:
English
Publication time:
11 / 2004