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The Perron-Frobenius theorem has numerous applications, including to Markov chains, economics, and ranking of webpages. In this paper, we develop a class of continuous-time distributed algorithms and a gossip algorithm, which enable each node i in an undirected and connected graph to compute the ith entry of the Perron-Frobenius eigenvector of a symmetric, Metzler, and irreducible matrix associated...
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...
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