Solving linear algebraic equations with limited computational power and network bandwidth

Shenyu Liu and Sonia Martínez
Systems and Control Letters, under review

Abstract:

This work introduces a distributed algorithm for finding least square (LS) so- lutions of linear algebraic equations (LAEs). Unlike the methods studied in the literature, we assume that our distributed algorithm has limited computa- tion power and network bandwidth, in the sense that each agent can only solve small-scale LAEs and the group of agents can only exchange messages of small size at a time. Our algorithm contains two layers of nested loops. A part of the solution is updated by a consensus algorithm in the inner loop, while an scheduling sequence in the outer loop decides which part of the solution to be updated. By appealing to the alternating projection theorem, we prove conver- gence of the proposed algorithm when the scheduling sequence is both spanning and periodic. The accuracy of our algorithm is verified through a numerical example.

File: main.pdf

Bib-tex entry:

@article{SL-SM:24-scl,
author = {S. Liu and S. Mart{\'\i}nez},
title = {Solving linear algebraic equations with limited computational power and network bandwidth},
journal = {System and Control Letters},
pages = {},
year = {2024},
note = {Submitted}
}