The power method is a basic method for computing the dominant eigenpair of a matrix. In this paper, we propose a structure-preserving power-like method for computing the dominant conjugate pair of purely imaginary eigenvalues and the corresponding eigenvectors of a large skew-symmetric matrix S, which works on S and its transpose alternately and is performed in real arithmetic. We establish the rigorous and quantitative convergence of the proposed power-like method, and prove that the approximations to the dominant eigenvalues converge twice as fast as those to the associated eigenvectors. Moreover, we develop a deflation technique to compute several complex conjugate dominant eigenpairs of S. Numerical experiments show the effectiveness and efficiency of the new method.

翻译：幂法是计算矩阵主特征对的基本方法。本文针对大规模斜对称矩阵S，提出了一种保持结构的类幂法，用于计算其主共轭纯虚特征值对及对应的特征向量。该方法交替作用于S及其转置，且完全在实数运算中执行。我们建立了所提类幂法的严格定量收敛性分析，并证明主特征值的逼近速度是相应特征向量逼近速度的两倍。此外，我们发展了一种收缩技术以计算S的多个复共轭主特征对。数值实验验证了新方法的有效性与高效性。