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arXiv · 2409.05048

A Power-like Method for Computing the Dominant Eigenpairs of Large Scale Real Skew-Symmetric Matrices

Qingqing Zheng
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Abstract

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.

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Qingqing Zheng. 2024-09-08. A Power-like Method for Computing the Dominant Eigenpairs of Large Scale Real Skew-Symmetric Matrices. https://arxiv.org/abs/2409.05048

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