论文标题
数值算法的并行性资源。版本1
Parallelism Resource of Numerical Algorithms. Version 1
论文作者
论文摘要
该论文致力于解决并行计算效率问题的方法。这种方法的理论基础是$ q $确定的概念。任何数值算法都有$ q $ - 确定的。该算法的$ Q $ - 确定性具有清晰的结构，可以方便地实现。 $ Q $ - 确定的由$ Q $ - terms组成。它们的数量等于输出数据项的数量。每个$ q $ - term介绍了根据输入数据计算输出数据项之一的所有可能方法。 我们还描述了一个软件$ q $系统，用于研究数值算法的并行性资源。该系统能够计算和比较数值算法的并行性资源。 $ q $ - 系统的应用显示在具有$ q $ - 确定剂不同结构的数值算法的示例上。此外，我们建议一种设计用于数值算法的并行程序的方法。此方法基于以$ q $确定的形式的数值算法表示。结果，我们可以完全使用该算法的并行性资源获得程序。这样的程序称为$ q $有效。 这项研究的结果可用于提高数值算法，方法以及并行计算系统上的算法问题的实施效率。
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 $Q$-determinant. Any numerical algorithm has a $Q$-determinant. The $Q$-determinant of the algorithm has clear structure and is convenient for implementation. The $Q$-determinant consists of $Q$-terms. Their number is equal to the number of output data items. Each $Q$-term describes all possible ways to compute one of the output data items based on the input data. We also describe a software $Q$-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 $Q$-system is shown on the example of numerical algorithms with different structures of $Q$-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 $Q$-determinant. As a result, we can obtain the program using the parallelism resource of the algorithm completely. Such programs are called $Q$-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.
