A Power-like Method for Computing the Dominant Eigenpairs of Large Scale Real Skew-Symmetric Matrices
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912018812895232 |
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| author | Zheng, Qingqing |
| author_facet | Zheng, Qingqing |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05048 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Power-like Method for Computing the Dominant Eigenpairs of Large Scale Real Skew-Symmetric Matrices Zheng, Qingqing Numerical Analysis 15A18, 65F15, 15A22 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. |
| title | A Power-like Method for Computing the Dominant Eigenpairs of Large Scale Real Skew-Symmetric Matrices |
| topic | Numerical Analysis 15A18, 65F15, 15A22 |
| url | https://arxiv.org/abs/2409.05048 |