A Power-like Method for Computing the Dominant Eigenpairs of Large Scale Real Skew-Symmetric Matrices
<|reference_start|>A Power-like Method for Computing the Dominant Eigenpairs of Large Scale Real Skew-Symmetric Matrices: 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.<|reference_end|>
@article{zheng2024a,
    title={A Power-like Method for Computing the Dominant Eigenpairs of Large Scale
  Real Skew-Symmetric Matrices},
    author={Qingqing Zheng},
    journal={arXiv preprint arXiv:2409.05048},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.05048},
    primaryClass={math.NA cs.NA}
}