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.
