  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.
