TY - JOUR
T1 - Solving linear algebraic equations with limited computational power and network bandwidth
AU - Liu, Shenyu
AU - Martinez, Sonia
N1 - Publisher Copyright:
© 2024 Elsevier B.V.
PY - 2025/2
Y1 - 2025/2
N2 - 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.
AB - 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.
KW - Distributed algorithm
KW - Least squares solutions
KW - Linear algebraic equations
UR - http://www.scopus.com/inward/record.url?scp=85213502229&partnerID=8YFLogxK
U2 - 10.1016/j.sysconle.2024.106008
DO - 10.1016/j.sysconle.2024.106008
M3 - Article
AN - SCOPUS:85213502229
SN - 0167-6911
VL - 196
JO - Systems and Control Letters
JF - Systems and Control Letters
M1 - 106008
ER -