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