A distributed algorithm based on multi-agent network for solving linear algebraic equation

Abstract

This paper presents a distributed discrete-time consensus algorithm based on multi-agent network to solve large-scale linear algebraic equation (LAE). The matrix in the LAE is divided into submatrices by the columns. Each agent in the network only has its own local data on the LAE and all the agents collaboratively find the solutions while they communicate with their neighbors. Based on the Lyapunov method for difference equation, the multi-agent network is analyzed to reach consensus at the solutions under some mild conditions. Compared with existing algorithms for LAE, the proposed algorithm is capable of solving large-scale distributed LAE problems with fixed step size.