Dynamical Systems Method for solving Ill-Conditioned Linear Algebraic Systems

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.