Abstract
In this paper we investigate the method of averaging functional corrections (AFCs), applied to the solution of a system of linear algebraic equations. This method, introduced by Sokolov [10,19], gives a possibility to accelerate the rates of convergence of a basic iterative method. We give some sufficient conditions for the convergence of the AFC method, which are weaker than the known one and illustrate that fact by several numerical examples. Also, we give a numerical example, which shows that the AFC method converges faster than the basic iterative method.
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