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Distributed least squares solver for network linear equations
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DOI：10.1016/j.automatica.2019.108798.png)
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Abstract
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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. (C) 2019 Elsevier Ltd. All rights reserved.
Keywords:
Distributed algorithms
Dynamical systems
Finite-time computation
Least squares
Linear equations
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