2024/01/26 by Jiang, Xin, Nguyen, Edward Duc Hien, Uribe, César A. +1
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2401.14596
In this paper, we study sparse factorization of the (scaled) square all-ones matrix J of arbitrary order. We introduce the concept of hierarchically banded matrices and propose two types of hierarchically banded factorization of J: 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~J 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.