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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求解非平稳线性不等式系统的可扩展并行算法

在本文中，考虑了一种用于求解线性不等式的非平稳系统的可扩展迭代投影型算法。非平稳系统被理解为一个大规模的不等式系统，其中系数和常数项在计算过程中可能会发生变化。所提出的并行算法使用泛化正交投影概念的伪投影概念。并行伪投影算法是使用并行 BSF 骨架实现的。基于 BSF 成本度量获得算法可扩展性边界的分析估计。大规模计算实验是在集群计算系统上进行的。获得的结果证实了所提出方法的效率。