Efficient Implementation of Numerical Algorithms Based on a Lexical Analyzer

The problem of improving the efficiency of parallel computations is a very topical one. In the article, we demonstrate the application of the concept of Q-determinant to the automatic creation of efficient implementations of algorithms. The Q-determinant concept relies on a unified representation of numerical algorithms through a Q-determinant. The Q-determinant allows the algorithm internal parallelism expression and evaluation and shows the method of parallel execution of the algorithm. We give the basic notions on the Q-determinant required for a better understanding of the research. This concept allows one to obtain a program that uses the parallelism resource of the algorithm in full. We call such a program a Q-efficient program. As an example of the design of Q-efficient programs, we describe the design of a software system consisting of a lexical analyzer and a program that executes aQ-efficient implementation. Finally, we present the results of experiments with the developed software system conducted on the “Tornado SUSU” supercomputer. After analyzing the results of these experiments, we determined the efficiency of the developed software system. The research described in the article leads to the conclusion that the application of the Q-determinant concept to the automatic creation of efficient programs is feasible.