Multiple Extremal Eigenpairs of Very Large Matrices by Monte Carlo   Simulation
  We present a new Monte Carlo algorithm that allows the simultaneous determination of a few extremal eigenpairs of a very large matrix. It extends the power method and uses a new sampling method, the sewing method, that does a large state space sampling as a succession of samplings from a smaller state space. We illustrate the new algorithm by its determination of the two largest eigenvalues of the transfer matrix of a square Ising model at the critical temperature for sizes from $16\times 16$ to $48\times 48$. 
T. E. Booth and J. E. Gubernatis