Multiple Extremal Eigenpairs of Very Large Matrices by Monte Carlo Simulation

T. E. Booth; J. E. Gubernatis

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arXiv · 0807.1273

Multiple Extremal Eigenpairs of Very Large Matrices by Monte Carlo Simulation

T. E. Booth·J. E. Gubernatis

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Abstract

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 $48\times 48$.

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BibTeX RIS

T. E. Booth, J. E. Gubernatis. 2008-07-08. Multiple Extremal Eigenpairs of Very Large Matrices by Monte Carlo Simulation. https://arxiv.org/abs/0807.1273

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