Dynamical systems gradient method for solving ill-conditioned linear algebraic systems - Hoang, N. S.; Ramm, Alexander G. (My University, 2010)
A version of the Dynamical Systems Method (DSM) for solving ill-conditioned linear algebraic systems is studied in this paper. An a priori and a posteriori stopping rules are justified. An algorithm for computing the solution using a spectral decomposition of the left-hand side matrix is proposed. Numerical results show that when a spectral decompositon of the left-hand side matrix is available or not computationally expensive to obtain the new method can be considered as an alternative to the Variational Regularization.
Keywords: Ill-conditioned linear algebraic systems; Dynamical Systems Method (DSM); Variational Regularization