Distributed Linear Equations Over Random Networks

Distributed linear algebraic equation over networks, where nodes hold a part of problem data and cooperatively solve the via node-to-node communications, is basic distributed computation task receiving an increasing research attention. Communications network have stochastic nature, with both temporal spatial dependence due to link failures, packet dropouts, or node recreation, etc. In this article, we study convergence rate protocols $\ast$ -mixing random network, dependencies between communications are allowed. When admits exact solutions, prove exponential projection consensus algorithm in mean-squared sense. Motivated by randomized Kaczmarz algorithm, also propose each randomly selects one row local equations for per iteration, establish convergence. no solution, that gradient-descent-like diminishing step-sizes can drive all nodes’ states least-squares solution at sublinear rate. These results collectively illustrate computations may overcome communication correlations if prototype algorithms enjoy certain contractive properties designed suitable parameters.