The APC Algorithm of Solving Large-Scale Linear Systems: A Generalized Analysis

A new algorithm called accelerated projection-based consensus (APC) has recently emerged as a promising approach to solve large-scale systems of linear equations in a distributed fashion. The algorithm adopts the federated architecture, and attracts increasing research interest; however, it's performance analysis is still incomplete, e.g., the error performance under noisy condition has not yet been investigated. In this paper, we focus on providing a generalized analysis by the use of the linear system theory, such that the error performance of the APC algorithm for solving linear systems in presence of additive noise can be clarified. We specifically provide a closed-form expression of the error of solution attained by the APC algorithm. Numerical results demonstrate the error performance of the APC algorithm, validating the presented analysis.