The Perron-Frobenius theorem: some of its applications

By Unnikrishna Pillai, Torsten Suel, Seunghun Cha. IEEE Signal Processing Magazine, 2005

335 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/04e456b03b4d13cc22042917fc65fb80ef8a5017

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Citations in the corpus

Adaptation, Learning, and Optimization over Networks (2014, methodology): “One important consequence of the primitiveness of A is that a famous result in matrix theory, known as the Perron-Frobenius Theorem [27, 113, 190] allows us to characterize the eigen-structure of A in the following manner — see Lemma F.”
Optimal Resource Allocation in Coordinated Multi-Cell Systems (2013, methodology): “This corresponds to the conditions SINRk = g −1 k (r ′ k) ∀k, which can be formulated as Kr linear equations and solved using the approach in [205].”
Supervised Learning Under Distributed Features (2018, background): “After sufﬁcient iterations, it is well-known that under some mild conditions on A [19], [47]–[50].”
Diffusion strategies for adaptation and learning over networks: an examination of distributed strategies and network behavior (2013, background): “For such networks, the left-stochastic combination matrix A will be what is called a primitive matrix [15], [29], [30], which in turn implies that A will have a unique eigenvalue at one while all other eigenvalues will have magnitude strictly less than one.”
Exact Diffusion for Distributed Optimization and Learning—Part I: Algorithm Development (2017, background): “This implies, in view of the PerronFrobenius theorem [14], [44], that there exists an eigenvector p satisfying”
Adaptive Networks (2014, neutral): “:3) ð A Þ ¼ 1 [11], [59], [101]–[103].”
Optimal Design of Energy-Efficient Multi-User MIMO Systems: Is Massive MIMO the Answer? (2014, methodology): “By utilizing a technique from [22], this equal-rate condition is met if and only if the uplink”