Computable convergence rate bound for ratio consensus algorithms
Abstract
The objective of the paper is to establish a computable upper bound for the almost sure convergence rate for a class of ratio consensus algorithms defined via column-stochastic matrices. Our result extends the works of Iutzeler et al. (2013) on similar bounds that have been obtained in a more restrictive setup with limited conclusions. The present paper complements the results of Gerencs\'er and Gerencs\'er (2021), identifying the exact almost sure convergence rate of a wide class of ratio consensus algorithms in terms of a spectral gap, which is, however, not computable in general. The upper bound provided in the paper will be compared to the actual rate of almost sure convergence experimentally on a range of modulated random geographic graphs with random local interactions.
Cite
@article{arxiv.2104.04802,
title = {Computable convergence rate bound for ratio consensus algorithms},
author = {Balázs Gerencsér},
journal= {arXiv preprint arXiv:2104.04802},
year = {2022}
}