On Distributed Solution of Ill-Conditioned System of Linear Equations under Communication Delays

This paper considers a distributed solution for a system of linear equations. The underlying peer-to-peer communication network is assumed to be undirected, however, the communication links are subject to potentially large but constant delays. We propose an algorithm that solves a distributed least-squares problem, which is equivalent to solving the system of linear equations. Effectively, the proposed algorithm is a pre-conditioned version of the traditional consensus-based distributed gradient descent (DGD) algorithm. We show that the accuracy of the solution obtained by the proposed algorithm is better than the DGD algorithm, especially when the system of linear equations is ill-conditioned.