Dynamical Systems Method for solving ill-conditioned linear algebraic systems

Details Dynamical Systems Method for solving ill-conditioned linear algebraic systems Dynamical Systems Method for solving ill-conditioned linear algebraic systems

2009-11-16

arxiv.org/abs/0911.3065v2

Mathematics

Numerical Analysis

26 pages

Scientific paper

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, JMAA,330 (2007),1338-1346, and proves convergence of the solution obtained by the iterative scheme.

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