Title: Dynamical systems method for solving ill-conditioned linear algebraic systems

Authors: Sapto W. Indratno, A.G. Ramm

Addresses: Department of Mathematics, Kansas State University, Manhattan, KS 66506-2602, USA. ' Department of Mathematics, Kansas State University, Manhattan, KS 66506-2602, USA

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.

Keywords: Hilbert matrix; FIEFK; Fredholm integral equations of the first kind; iterative regularisation; variational regularisation; discrepancy principle; DSM; dynamical systems method; ill-conditioned linear algebraic systems.

DOI: 10.1504/IJCSM.2009.030911

International Journal of Computing Science and Mathematics, 2009 Vol.2 No.4, pp.308 - 333

Published online: 11 Jan 2010 *

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