A distributed algorithm for efficiently solving linear equations and its applications (Special Issue JCW)

A distributed algorithm is proposed for solving a linear algebraic equation Ax = b over a multi-agent network, where A E R-n*n and the equation has a unique solution x* is an element of R-n. Each agent knows only a subset of the rows of [A b], controls a state vector xi(t) of size smaller than n and is able to receive information from its nearby neighbors. Neighbor relations are characterized by time -dependent directed graphs. It is shown that for a large class of time-varying networks, the proposed algorithm enables each agent to recursively update its own state by only using its neighbors' states such that all xi(t) converge exponentially fast to a specific part of x(i)(t) of interest to agent i. Applications of the proposed algorithm include solving the least square solution problem and the network localization problem. (C) 2016 Elsevier B.V. All rights reserved.