Solving ill-conditioned linear algebraic systems by the dynamical systems method (DSM)
For researchers solving ill-conditioned linear systems, this work offers a simpler iterative alternative to variational regularization, though it is an incremental improvement over existing DSM approaches.
The paper presents an iterative scheme for the Dynamical Systems Method (DSM) that avoids solving a Cauchy problem and eliminates the need to find a regularization parameter via a nonlinear equation. Numerical experiments show DSM competes favorably with Variational Regularization for ill-conditioned linear systems.
An iterative scheme for the Dynamical Systems Method (DSM) is given such that one does not have to solve the Cauchy problem occuring in the application of the DSM for solving ill-conditioned linear algebraic systems. The novelty of the algorithm is that the algorithm does not have to find the regularization parameter $a$ by solving a nonlinear equation. Numerical experiments show that DSM competes favorably with the Variational Regularization.