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

TL;DR

This paper provides a comprehensive analysis of the APC algorithm for large-scale linear systems, including its error behavior under noisy conditions, supported by theoretical derivations and numerical validation.

Contribution

It offers a generalized, linear system theory-based analysis of the APC algorithm's error performance, especially under additive noise, with a closed-form error expression.

Findings

Error performance of APC under noise is characterized.

Closed-form expression for solution error is derived.

Numerical results validate the theoretical analysis.

Abstract

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.