Publicação
Isospectral reductions of non-negative matrices
| 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. |
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| 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 |
| 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. |
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