Iterative Algorithm for Solving of Linear Algebraic Equations Systems without Multi-bit Multiplication Operation

An iterative method of the systems of the linear algebraic equations solution, excluding the multi-bit multiplication operation while designing the special-purpose computing facilities is considered. Algorithmization of the iteration process is based on the use of the first order delta-transformations with the variable quantum that can significantly reduce the number of iterations in comparison with the using of the constant quantum. The optimal estimations characterizing the duration of idealized iterative loops with constant quantum of a certain value are formed. In theoretical justification quasi-optimal conditions determining a way of the representation a sequence of variable quanta values in the loops and based on using two or four idealized iterations within each loop are developed for the purpose of the real processes. Besides the quanta values shall be represented in the form of a shift operation? that allows realizing the implementation of the iterative process without using the multiplication of the multi-bit codes. There are also effective ways to complete the iteration in each loop. The findings of investigation of the iterative solution of various systems of the linear algebraic equations different with convergence rate are given in the work. The possibility of reduction the number of iterations in comparison with the using the delta-transformations with the constant quantum to hundreds -- thousands of times is shown when ensuring the identical accuracy. The number of iterations with variable quantum is to a considerable extent approximate the number of iterations to the simple iteration method.