用蒙特卡罗模拟求超大型矩阵的多重极值特征对
Multiple Extremal Eigenpairs of Very Large Matrices by Monte Carlo Simulation
摘要：
我们提出了一种新的蒙特卡罗算法，允许同时确定一个非常大的矩阵的几个极值特征对。它扩展了幂方法，并使用了一种新的采样方法，缝纫方法，它做了一个大的状态空间采样作为一个连续的采样从一个较小的状态空间。我们说明了新的算法，其确定的两个最大的特征值的转移矩阵的平方伊辛模型在临界温度的尺寸从$16\times 16$到$48\times 48$。
英文摘要：
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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