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Isospectral reductions of non-negative matrices

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Resumo:Isospectral reduction is an important tool for network/matrix analysis as it reduces the dimension of a matrix/network while preserving all 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 reduction. This scheme can be advantageous when there is more than one eigenvalue near 1, precisely the case where iterative methods perform poorly. In addition we give a partial explanation why this scheme should work well, showing that in some situations isospectral reduction improves the spectral gap.
Autores principais:Baraviera, Alexandre
Outros Autores:Duarte, Pedro; Shu, Longmei; Torres, M. J.
Assunto:Isospectral reductions Stochastic matrices Stationary measure
Ano:2025
País:Portugal
Tipo de documento:artigo
Tipo de acesso:acesso aberto
Instituição associada:Universidade do Minho
Idioma:inglês
Origem:RepositóriUM - Universidade do Minho

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