论文标题
求解大规模线性系统的APC算法：广义分析
The APC Algorithm of Solving Large-Scale Linear Systems: A Generalized Analysis
论文作者
论文摘要
一种名为基于投影的共识（APC）的新算法最近已成为一种有前途的方法，可以以分布式方式求解线性方程式的大规模系统。该算法采用了联邦建筑，并引起了越来越多的研究兴趣。但是，它的性能分析仍然不完整，例如，在嘈杂条件下的错误性能尚未得到研究。在本文中，我们专注于通过使用线性系统理论提供广义分析，以便可以阐明APC算法用于求解线性系统的误差性能。我们明确提供了APC算法达到的解决方案误差的封闭式表达。数值结果证明了APC算法的误差性能，从而验证了所提出的分析。
A new algorithm called accelerated projection-based consensus (APC) has recently emerged as a promising approach to solve large-scale systems of linear equations in a distributed fashion. The algorithm adopts the federated architecture, and attracts increasing research interest; however, it's performance analysis is still incomplete, e.g., the error performance under noisy condition has not yet been investigated. In this paper, we focus on providing a generalized analysis by the use of the linear system theory, such that the error performance of the APC algorithm for solving linear systems in presence of additive noise can be clarified. We specifically provide a closed-form expression of the error of solution attained by the APC algorithm. Numerical results demonstrate the error performance of the APC algorithm, validating the presented analysis.
