Dynamical Systems Method for solving ill-conditioned linear algebraic systems
For researchers dealing with ill-posed problems, this provides a new iterative approach with theoretical guarantees, though it is an incremental extension of existing DSM work.
The paper applies the Dynamical Systems Method (DSM) to solve ill-conditioned linear algebraic systems, proposing a new iterative scheme with justified a posteriori stopping rules and proving convergence.
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.