  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.

Optimization and Control