Sparse factorization of the square all-ones matrix of arbitrary order
Optimization and Control
2024-11-19 v2
Abstract
In this paper, we study sparse factorization of the (scaled) square all-ones matrix of arbitrary order. We introduce the concept of hierarchically banded matrices and propose two types of hierarchically banded factorization of : the reduced hierarchically banded (RHB) factorization and the doubly stochastic hierarchically banded (DSHB) factorization. Based on the DSHB factorization, we propose the sequential doubly stochastic (SDS) factorization, in which~ is decomposed as a product of sparse, doubly stochastic matrices. Finally, we discuss the application of the proposed sparse factorizations to the decentralized average consensus problem and decentralized optimization.
Keywords
Cite
@article{arxiv.2401.14596,
title = {Sparse factorization of the square all-ones matrix of arbitrary order},
author = {Xin Jiang and Edward Duc Hien Nguyen and César A. Uribe and Bicheng Ying},
journal= {arXiv preprint arXiv:2401.14596},
year = {2024}
}