Solving Least Squares for Linear Equations over Strongly Connected Directed Networks
Mohammad Jahvani, Martin Guay · 2020
In this paper, we introduce a distributed continuous-time flow on directed networks for the computation of least-squares solution to a linear algebraic equation of the form Ax=b where A has full column rank. It is assumed that each one of the n autonomous agents only knows a subset of the partitioned matrix [A b]. Each agent in the network is able to send information to certain other agents called its “out-neighbors”. Neighbor relations are characterized by a directed graph G whose vertices correspond to the labels of agents and whose edges depict the neighbor relations. It is shown that for any such matrix A and any strongly connected neighbor graph, the estimates of all agents in the proposed algorithm converge exponentially to the desired solution (A'A)-1A'b, even if only one of the agents across the network uses a nonzero and sufficiently small constant step-size.