ABOUT THE FUNCTIONING OF THE SPECIAL-PURPOSE CALCULATING UNIT BASED ON THE LINEAR SYSTEM SOLUTION USING THE FIRST ORDER DELTA-TRANSFORMATIONS

摘要

This paper discusses the theoretical representations of special-purpose calculating unit functioning for the iteration solution of linear systems using the first order delta-transformations and variable quantum. It is considered the algorithm for iterative solution of linear systems based on the first order delta-transformations and variable quantum is adapted for implementation in a special-purpose calculating unit. A special feature of special-purpose calculating unit functioning based on this algorithm is the implementation of the introduction at the beginning of each cycle l of a new variable quantum value that is reflected in the current cycle when the residual values and the unknown variable are formed by shifting them to the left by 1 or 2 bits. Formation of unknown variables in the unit is carried out by adding or subtracting the signs of quantum of the first and second variables differences, taking at each iteration the values ? 1. This feature of variable normalization represents the possibility of organizing a computational process on the basis of an integer data representation. At the final step of the algorithm operation in the unit, it is possible to bring the values of the variables to the original real form, taking into account the weight of the minimum transformation quantum. With the orientation to FPGA, comparative estimates are obtained for the hardware and time resources of the developed algorithm and comprehensive comparative estimate of the effectiveness for special-purpose calculating unit functioning. In this paper for the developed algorithm of the unit functioning, it is shown that it is possible to reduce the execution of one iteration and the iterative process as a whole, the amount of hardware resources and generally improve the efficiency in comparison with the special-purpose calculating unit functioning based on the simple iteration method.