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Article title THE ITERATIVE METHOD FOR SOLVING SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS, EXCLUSIVE THE MULTI-BIT MULTIPLICATION OPERATION
Authors P.P. Kravchenko, L.V.Pirskaya
Section SECTION V. MODELLING OF COMPLEX SYSTEMS
Month, Year 07, 2014 @en
Index UDC 621.376.57
DOI
Abstract In work it is considered the iterative method for solving systems of linear algebraic equations, exclusive the multi-bit multiplication operation in the design of embedded systems. It is developed a method of organizing an iterative process for solving systems of algebraic equations with using the first order delta-transformations with variable quantum. The method is based on the optimal theoretical estimates characterizing the idealized iterative cycles duration and quanta variable weight of initial maximum value of the misalignment. It is developed quasioptimal conditions defining two or four iterations in each cycle for realization real iterative working processes. Moreover, quanta values should be presented in a form of 2-s ,s ∩ N that allow expressing the multiplication of coefficient matrix on a quantum in a form of shift operation on S bitsat each iteration. This quantum representation allows realizing the execution of iterative process without the use of multi-bit multiplication operation. The paper presents experimental results for the various systems of linear algebraic equations with the different rate of convergence. It is showed the possibility of reducing the number of iterations compared with the delta transformation with a fixed quantum in thousands of times with the same accuracy. And it is largely approximate to the number of iteration for the simple iteration method.

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Keywords Iterative methods; systems of linear algebraic equations; delta transformation of the first order; specialized computing devices.
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