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Algebraic Connectivity Estimation Based on Decentralized Inverse Power Iteration
Author(s) -
Wei Yue,
Fang Hao,
Chen Jie,
Xin Bin
Publication year - 2017
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1388
Subject(s) - algebraic connectivity , conjugate gradient method , algebraic graph theory , convergence (economics) , mathematical optimization , network topology , computation , mathematics , power iteration , inverse , rate of convergence , inversion (geology) , scheme (mathematics) , algebraic number , topology (electrical circuits) , computer science , graph , algorithm , iterative method , theoretical computer science , laplacian matrix , channel (broadcasting) , structural basin , economic growth , computer network , mathematical analysis , biology , operating system , paleontology , geometry , combinatorics , economics
In this work, we propose a new scheme to estimate the algebraic connectivity of the graph describing the network topology of a multi‐agent system. We consider network topologies modeled by undirected graphs. The main idea is to propose a new decentralized conjugate gradient algorithm and a decentralized compound inverse power iteration scheme. The matrix inversion computation in this scheme is replaced by solving the non‐homogeneous linear equations relying on the proposed decentralized conjugate gradient algorithm. With this scheme, we can achieve a fast convergence rate in estimating the algebraic connectivity by setting the parameter μ properly. Simulation results demonstrate the effectiveness of the proposed scheme.