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Article title METHOD OF ITERATION SOLVING OF LINEAR ALGEBRAIC EQUATIONS SYSTEMS USING THE SECOND ORDER DELTA-TRANSFORMATIONS
Authors P.P. Kravchenko, L.V. Pirskaya
Section SECTION II. MODELING OF COMPLEX SYSTEMS
Month, Year 06, 2015 @en
Index UDC 621.376.57
DOI
Abstract In this paper it is considered the iterative method for solving systems of linear algebraic equations with constant and variable free terms, based on using the second order delta-transformations with variable quantum. Using this methodology allows to significantly reduce the number of iterations than using constant quantum and to implement the computing process in a special-purpose computing without the multidigit multiplication operation. For the first time it is represented the basic theoretical principles, substantiating the approximate the problem solution of minimizing the number of iterations using the variable quantum. In the theoretical substantiation it is formulated assessments, describing an optimized duration of idealized iterative cycles with constant quantum of a certain value. To implement real processes it is developed integer parameters estimates that determine how the sequence variables quanta in cycles is set and based on using four or eight idealized iterations in each cycle. There are the conditions for the efficient completion of the iterative processes in cycles. The paper presents the computer simulation results of the iterative solutions of different linear algebraic equations systems with different speeds of convergence. It is presented the results of computer simulation for solving the linear algebraic equations systems with harmonic free terms, showed the benefits of largest solutions implemented step in the steady process in ~ 80 times by using the second order delta-transformations in comparison with using the first order delta-transformations.

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Keywords Iterative methods; solving of linear algebraic equations systems; delta-transformations of the second order; delta-transformations of the first order; special-purpose computer; FPGA.
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