多重极值特征对的幂方法
Multiple Extremal Eigenpairs by the Power Method
摘要：
我们报告的生产和基准的几个改进的电源方法，使计算的多个极值特征对非常大的矩阵。在这些改进中，我们使用了布思的观测结果，该观测结果使得计算多达10个$^{th}$本征对成为可能，用于模拟核反应堆稳态中子输运的简单测试问题。在这里，我们总结了我们的技术和努力，主要是确定两个最大或两个最小的特征对。为了说明该技术的有效性，我们确定了循环矩阵的两个极值特征对，二维伊辛模型的转移矩阵，和一维哈伯德模型的哈密顿矩阵。
英文摘要：
We report the production and benchmarking of several refinements of the power method that enable the computation of multiple extremal eigenpairs of very large matrices. In these refinements we used an observation by Booth that has made possible the calculation of up to the 10$^{th}$ eigenpair for simple test problems simulating the transport of neutrons in the steady state of a nuclear reactor. Here, we summarize our techniques and efforts to-date on determining mainly just the two largest or two smallest eigenpairs. To illustrate the effectiveness of the techniques, we determined the two extremal eigenpairs of a cyclic matrix, the transfer matrix of the two-dimensional Ising model, and the Hamiltonian matrix of the one-dimensional Hubbard model.
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