Parallelism Resource of Numerical Algorithms. Version 1
Abstract
The paper is devoted to an approach to solving a problem of the efficiency of parallel computing. The theoretical basis of this approach is the concept of a -determinant. Any numerical algorithm has a -determinant. The -determinant of the algorithm has clear structure and is convenient for implementation. The -determinant consists of -terms. Their number is equal to the number of output data items. Each -term describes all possible ways to compute one of the output data items based on the input data. We also describe a software -system for studying the parallelism resource of numerical algorithms. This system enables to compute and compare the parallelism resources of numerical algorithms. The application of the -system is shown on the example of numerical algorithms with different structures of -determinants. Furthermore, we suggest a method for designing of parallel programs for numerical algorithms. This method is based on a representation of a numerical algorithm in the form of a -determinant. As a result, we can obtain the program using the parallelism resource of the algorithm completely. Such programs are called -effective. The results of this research can be applied to increase the implementation efficiency of numerical algorithms, methods, as well as algorithmic problems on parallel computing systems.
Cite
@article{arxiv.2207.11915,
title = {Parallelism Resource of Numerical Algorithms. Version 1},
author = {Valentina N. Aleeva and Rifkhat Zh. Aleev},
journal= {arXiv preprint arXiv:2207.11915},
year = {2022}
}