1 research outputs found
A Distributed Algorithm for Solving Linear Algebraic Equations Over Random Networks
In this paper, we consider the problem of solving linear algebraic equations
of the form among multi agents which seek a solution by using local
information in presence of random communication topologies. The equation is
solved by agents where each agent only knows a subset of rows of the
partitioned matrix . We formulate the problem such that this formulation
does not need the distribution of random interconnection graphs. Therefore,
this framework includes asynchronous updates or unreliable communication
protocols without B-connectivity assumption. We apply the random
Krasnoselskii-Mann iterative algorithm which converges almost surely and in
mean square to a solution of the problem for any matrices and and any
initial conditions of agents' states. We demonestrate that the limit point to
which the agents' states converge is determined by the unique solution of a
convex optimization problem regardless of the distribution of random
communication graphs. Eventually, we show by two numerical examples that the
rate of convergence of the algorithm cannot be guaranteed.Comment: 10 pages, 2 figures, a preliminary version of this paper appears
without proofs in the Proceedings of the 57th IEEE Conference on Decision and
Control, Miami Beach, FL, USA, December 17-19, 201