Solving linear algebraic equations with limited computational power and network bandwidth

Shenyu Liu*, Sonia Martinez

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This work introduces a distributed algorithm for finding least squares (LS) solutions of linear algebraic equations (LAEs). Unlike the methods studied in the literature, we assume that our distributed algorithm has limited computation 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 convergence of the proposed algorithm when the scheduling sequence is both spanning and periodic. The accuracy of our algorithm is verified through a numerical example.

Original languageEnglish
Article number106008
JournalSystems and Control Letters
Volume196
DOIs
Publication statusPublished - Feb 2025

Keywords

  • Distributed algorithm
  • Least squares solutions
  • Linear algebraic equations

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Liu, S., & Martinez, S. (2025). Solving linear algebraic equations with limited computational power and network bandwidth. Systems and Control Letters, 196, Article 106008. https://doi.org/10.1016/j.sysconle.2024.106008