Abstract

In this paper, a scalable iterative projection-type algorithm for solving non-stationary systems of linear inequalities is considered. A non-stationary system is understood as a large-scale system of inequalities in which coefficients and constant terms can change during the calculation process. The proposed parallel algorithm uses the concept of pseudo-projection which generalizes the notion of orthogonal projection. The parallel pseudo-projection algorithm is implemented using the parallel BSF-skeleton. An analytical estimation of the algorithm scalability boundary is obtained on the base of the BSF cost metric. The large-scale computational experiments were performed on a cluster computing system. The obtained results confirm the efficiency of the proposed approach.

中文翻译：

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线性不等式非平稳系统的可扩展并行算法

摘要

本文考虑了求解线性不等式非平稳系统的可伸缩迭代投影型算法。非平稳系统被理解为不等式的大规模系统，其中系数和常数项可以在计算过程中改变。所提出的并行算法使用伪投影的概念，该概念概括了正交投影的概念。并行伪投影算法是使用并行BSF骨架实现的。在BSF成本度量的基础上，获得了算法可伸缩性边界的分析估计。大型计算实验是在群集计算系统上进行的。获得的结果证实了该方法的有效性。