In this paper, we study the problem of finding the least square solutions of over-determined linear algebraic equations over networks in a distributed manner. Each node has access to one of the linear equations and holds a dynamic state. We first propose a distributed least square solver over connected undirected interaction graphs and establish a necessary and sufficient on the step-size under which the algorithm exponentially converges to the least square solution. Next, we develop a distributed least square solver over strongly connected directed graphs and show that the proposed algorithm exponentially converges to the least square solution provided the step-size is sufficiently small. Moreover, we develop a finite-time least square solver by equipping the proposed algorithms with a finite-time decentralized computation mechanism. The theoretical findings are validated and illustrated by numerical simulation examples.
@article{arxiv.1810.00156,
title = {Distributed Least Squares Solver for Network Linear Equations},
author = {Tao Yang and Jemin George and Jiahu Qin and Xinlei Yi and Junfeng Wu},
journal= {arXiv preprint arXiv:1810.00156},
year = {2019}
}