Dynamical systems gradient method for solving ill-conditioned linear   algebraic systems
  A version of the Dynamical Systems Method (DSM) for solving ill-conditioned linear algebraic systems is studied in this paper. An {\it a priori} and {\it 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. 
N. S. Hoang, and A. G. Ramm