Dynamical systems method for solving ill-conditioned linear algebraic systems

Authors:
Sapto W. Indratno;A. G. Ramm
Affiliations:
Department of Mathematics, Kansas State University, Manhattan, KS 66506-2602, USA.;Department of Mathematics, Kansas State University, Manhattan, KS 66506-2602, USA
Venue:
International Journal of Computing Science and Mathematics
Year:
2009

Citing 2
Cited 1

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Abstract

A new method, the Dynamical Systems Method (DSM), justified recently, is applied to solving Ill-Conditioned Linear Algebraic System (ICLAS). The DSM gives a new approach to solving a wide class of ill-posed problems. In this paper a new iterative scheme for solving ICLAS is proposed. This iterative scheme is based on the DSM solution. An a posteriori stopping rules for the proposed method is justified. This paper also gives an a posteriori stopping rule for a modified iterative scheme developed in A.G. Ramm, Jour. Math. Anal. Appl., Vol. 330 (2007), pp.1338-1346, and proves convergence of the solution obtained by the iterative scheme.