Distributed Algorithm for Linear Least Squares Problems via Iteratively Preconditioning by Successive Over-Relaxation
Abstract
This paper focuses on a novel distributed optimization algorithm for solving multi-agent linear least squares problems within a server-agent framework. Distributed methods are particularly suited to large-scale systems. The computational tasks can be partitioned across agents, while local data of one agent remain inaccessible to others. The proposed approach employs an iterative preconditioning scheme with the successive over-relaxation technique, leading to a substantial reduction of the number of iterations required for convergence, which presents a critical advantage where server-agent communication is costly. Theoretical convergence proof of the proposed algorithm is presented. Finally, benchmark problems are tested to demonstrate the performance comparison of the proposed approach over several prominent distributed methods.
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BibTeX
@misc{liu2026distributed,
title = {{Distributed Algorithm for Linear Least Squares Problems via Iteratively Preconditioning by Successive Over-Relaxation}},
author = {Tianchen Liu and Kushal Chakrabarti},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25872},
eprint = {2610.25872},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25872},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Distributed Algorithm for Linear Least Squares Problems via Iteratively Preconditioning by Successive Over-Relaxation
AU - Tianchen Liu
AU - Kushal Chakrabarti
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25872
UR - https://arxiv.org/abs/2610.25872
AB - This paper focuses on a novel distributed optimization algorithm for solving multi-agent linear least squares problems within a server-agent framework. Distributed methods are particularly suited to large-scale systems. The computational tasks can be partitioned across agents, while local data of one agent remain inaccessible to others. The proposed approach employs an iterative preconditioning scheme with the successive over-relaxation technique, leading to a substantial reduction of the number of iterations required for convergence, which presents a critical advantage where server-agent communication is costly. Theoretical convergence proof of the proposed algorithm is presented. Finally, benchmark problems are tested to demonstrate the performance comparison of the proposed approach over several prominent distributed methods.
ER -