On the rate convergence of combined iterative methods of variational type

Iterative solution method of variational type for the sets of linear equations is investigated. The rate of convergence of the method is studied by usage of general results of stability theory. An implicit variant of the two-stage gradient descent method is proposed. On the basis of asymptotical analysis a new modification of the original method is constructed, for which the rate of the convergence is accelerated. The efficiency of the method is investigated on the model boundary value problem and the results of numerical experiments are given.