Improving Parallel Computing Efficiency

Abstract

In this paper some approach to solving a problem of the efficiency of parallel computing is considered on the base of the concept of a Q-determinant. Any numerical algorithm has a Q-determinant that is convenient for implementation. The content of every Q-determinant are Q-terms that number is equal to the number of output data items. On the base of the input data each of Q-terms allows for the considering of all possible ways to compute one of the output data items. We also describe a software Q-system for studying the parallelism resource of numerical algorithms. Furthermore, we suggest a method for designing of parallel programs for numerical algorithms. As a result, we can obtain the program with complete the parallelism resource of the algorithm. Such programs are called Q-effective. We also suggest the technology of Q-effective programming. On the base of this research we can increase the efficiency of implementation of numerical algorithms, methods, as well as algorithmic problems on parallel computing systems.