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A distributed algorithm for least mean square (LMS) can be used indistributed signal estimation and in distributed training for multivariateregression models. The convergence speed of an algorithm is a critical factorbecause a faster algorithm requires less communications overhead and it resultsin a narrower network bandwidth. The goal of this paper is to present that useof Chebyshev periodical successive over-relaxation (PSOR) can acceleratedistributed LMS algorithms in a naturally manner. The basic idea of ChbyshevPSOR is to introduce index-dependent PSOR factors that control the spectralradius of a matrix governing the convergence behavior of the modifiedfixed-point iteration. Accelerations of convergence speed are empiricallyconfirmed in a wide range of networks, such as known small graphs (e.g., Karategraph), and random graphs, such as Erdos-Renyi (ER) random graphs andBarabasi-Albert random graphs.

Acceleration of Cooperative Least Mean Square via Chebyshev Periodical Successive Over-Relaxation