  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.
