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arXiv · 1810.00156

Distributed Least Squares Solver for Network Linear Equations

Tao Yang·Jemin George·Jiahu Qin·Xinlei Yi·Junfeng Wu
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Abstract

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.

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Tao Yang, Jemin George, Jiahu Qin, Xinlei Yi, Junfeng Wu. 2018-09-29. Distributed Least Squares Solver for Network Linear Equations. https://arxiv.org/abs/1810.00156

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