  A distributed algorithm for least mean square (LMS) can be used in
distributed signal estimation and in distributed training for multivariate
regression models. The convergence speed of an algorithm is a critical factor
because a faster algorithm requires less communications overhead and it results
in a narrower network bandwidth. The goal of this paper is to present that use
of Chebyshev periodical successive over-relaxation (PSOR) can accelerate
distributed LMS algorithms in a naturally manner. The basic idea of Chbyshev
PSOR is to introduce index-dependent PSOR factors that control the spectral
radius of a matrix governing the convergence behavior of the modified
fixed-point iteration. Accelerations of convergence speed are empirically
confirmed in a wide range of networks, such as known small graphs (e.g., Karate
graph), and random graphs, such as Erdos-Renyi (ER) random graphs and
Barabasi-Albert random graphs.
