Algorithm of Iterative Solution of Linear Algebraic Equations Systems Based on the Second Order Delta-Transformation for Specialized Computers of Real-Time Systems

Pavel Pavlovich Kravchenko, Liubov Vladimirovna Pirskaya and Nail’ Shavkyatovish Khusainov

Southern Federal University, Russia, 344006, Rostov-on-Don, Bolshaya Sadovaya Str., 105/42.

DOI : http://dx.doi.org/10.13005/bbra/2201

ABSTRACT: The study discusses iteration method for solution of algebraic equation systems with constant and variable free terms based on the second order delta-transformation with variable quantum. Use of that methodology allows to significantly decrease number of iterations, as compared with constant quantum, and realize computing process in a specialized computer without devices for multiplication of multi-bit codes. The study for the first time presents theoretical points justifying approximate solution of problem of minimization of number of iterations in a case of implementation of variable quantum. Theoretical justification forms evaluations, which characterize optimized operation of idealized iteration cycles with constant quantum of a certain value. For implementation of real processes integer evaluations of parameters are developed, which define a method for specification of sequence of values of variable quantum in cycles and which are based on four or eight idealized iterations per cycle. The study proposes conditions for effective ending of iteration processes in cycles. The study presents results of computer simulation of iteration solution of various algebraic equation systems, which differ in convergence rate. The results of computer simulation of linear algebraic equation systems (linear systems) with harmonic free terms are presented, which demonstrate an advantage in a value of realized step of solution in steady-state process in, approximately, 80 times in a case of implementation of the second order delta-transformation as compared with implementation of the first order delta-transformation.

KEYWORDS: Iterative methods; Solution of linear algebraic equation systems; The second order delta-transformation; The first order delta-transformation; Specialized computers; PLD

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