Gerencsér, Balázs and Gerencsér, László (2020) Tight bounds on the convergence rate of generalized ratio consensus algorithms. IEEE TRANSACTIONS ON AUTOMATIC CONTROL. ISSN 00189286

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Abstract
The problems discussed in this paper are motivated by general ratio consensus algorithms, introduced by Kempe, Dobra, and Gehrke (2003) in a simple form as the pushsum algorithm, later extended by B´en´ezit et al. (2010) under the name weighted gossip algorithm. We consider a communication protocol described by a strictly stationary, ergodic, sequentially primitive sequence of nonnegative matrices, applied iteratively to a pair of fixed initial vectors, the components of which are called values and weights defined at the nodes of a network. The subject of ratio consensus problems is to study the asymptotic properties of ratios of values and weights at each node, expecting convergence to the same limit for all nodes. The main results of the paper provide upper bounds forthe rate of the almost sure exponential convergence in terms of the spectral gap associated with the given sequence of random matrices. It will be shown that these upper bounds are sharp. Our results complement previous results of Picci and Taylor (2013) and Iutzeler, Ciblat and Hachem (2013).
Item Type:  Article 

Subjects:  Q Science / természettudomány > QA Mathematics / matematika 
SWORD Depositor:  MTMT SWORD 
Depositing User:  MTMT SWORD 
Date Deposited:  01 Mar 2021 12:16 
Last Modified:  25 Apr 2023 09:27 
URI:  http://real.mtak.hu/id/eprint/121782 
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