Isospectral reductions of non-negative matrices

Alexandre Baraviera, Pedro Duarte, Longmei Shu and Maria Joana Torres

Applied Mathematics and Computation, 2025, vol. 499, issue C

Abstract: Isospectral reduction is an important tool for network/matrix analysis as it reduces the dimension of a matrix/network while preserving its eigenvalues and eigenvectors. The main contribution of this manuscript is a proposed algorithmic scheme to approximate the stationary measure of a stochastic matrix based on isospectral reductions. We run numerical experiments that indicate this scheme is advantageous when there is more than one eigenvalue near 1, precisely the case where iterative methods perform poorly. We give a partial explanation why this scheme should work well, showing that in some situations isospectral reduction improves the spectral gap.

Keywords: Isospectral reductions; Stochastic matrices; Stationary measure (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:499:y:2025:i:c:s0096300325001298

DOI: 10.1016/j.amc.2025.129402

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