Memory-Enhanced Distributed Accelerated Algorithms for Coordinated Linear Computation

Abstract

In this paper, a memory-enhanced distributed accelerated algorithm is proposed for solving large-scale systems of linear equations within the context of multi-agent systems. By employing a local predictor consisting of a linear combination of the nodes' current and previous values, the inclusion of two memory taps can be characterized such that the convergence of the distributed solution algorithm for coordinated computation is accelerated. Moreover, consensus-based convergence results are established by leveraging an analysis of the spectral radius of an augmented iterative matrix associated with the error system that arises from solving the equation. In addition, the connection between the convergence rate and the tunable parameters is developed through an examination of the spectral radius of the iterative matrix, and the optimal mixing parameter is systematically derived to achieve the fastest convergence rate. It is shown that despite whether the linear equation of interest possesses a unique solution or multiple solutions, the proposed distributed algorithm exhibits exponential convergence to the solution, without dependence on the initial conditions. In particular, both the theoretical analysis and simulation examples demonstrate that the proposed distributed algorithm can achieve a faster convergence rate than conventional distributed algorithms for the coordinated linear computation, provided that adjustable parameters are appropriately selected.