Distributed Estimation of Graph Spectrum
| Autor: | Yang, Mu, Tang, Choon Yik |
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| Rok vydání: | 2015 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we develop a two-stage distributed algorithm that enables nodes in a graph to cooperatively estimate the spectrum of a matrix $W$ associated with the graph, which includes the adjacency and Laplacian matrices as special cases. In the first stage, the algorithm uses a discrete-time linear iteration and the Cayley-Hamilton theorem to convert the problem into one of solving a set of linear equations, where each equation is known to a node. In the second stage, if the nodes happen to know that $W$ is cyclic, the algorithm uses a Lyapunov approach to asymptotically solve the equations with an exponential rate of convergence. If they do not know whether $W$ is cyclic, the algorithm uses a random perturbation approach and a structural controllability result to approximately solve the equations with an error that can be made small. Finally, we provide simulation results that illustrate the algorithm. Comment: 15 pages, 2 figures |
| Databáze: | arXiv |
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