2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164462We 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 $48\times 48$.4 pages, no figuresStatistical MechanicsStrongly Correlated ElectronsComputational Physicstext