A Contour Integral-Based Algorithm for Computing Generalized Singular Values
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866908872281686016 |
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| author | Liu, Yuqi Shan, Xinyu Shao, Meiyue |
| author_facet | Liu, Yuqi Shan, Xinyu Shao, Meiyue |
| contents | We propose a contour integral-based algorithm for computing a few singular values of a matrix or a few generalized singular values of a matrix pair. Mathematically, the generalized singular values of a matrix pair are the eigenvalues of an equivalent Hermitian-definite matrix pencil, known as the Jordan-Wielandt matrix pencil. However, direct application of the FEAST algorithm does not fully exploit the structure of this problem. We analyze several projection strategies on the Jordan-Wielandt matrix pencil, and propose an effective and robust scheme tailored to GSVD. Both theoretical analysis and numerical experiments demonstrate that our algorithm achieves rapid convergence and satisfactory accuracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00121 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Contour Integral-Based Algorithm for Computing Generalized Singular Values Liu, Yuqi Shan, Xinyu Shao, Meiyue Numerical Analysis 15A18, 65F15, 65F50 We propose a contour integral-based algorithm for computing a few singular values of a matrix or a few generalized singular values of a matrix pair. Mathematically, the generalized singular values of a matrix pair are the eigenvalues of an equivalent Hermitian-definite matrix pencil, known as the Jordan-Wielandt matrix pencil. However, direct application of the FEAST algorithm does not fully exploit the structure of this problem. We analyze several projection strategies on the Jordan-Wielandt matrix pencil, and propose an effective and robust scheme tailored to GSVD. Both theoretical analysis and numerical experiments demonstrate that our algorithm achieves rapid convergence and satisfactory accuracy. |
| title | A Contour Integral-Based Algorithm for Computing Generalized Singular Values |
| topic | Numerical Analysis 15A18, 65F15, 65F50 |
| url | https://arxiv.org/abs/2401.00121 |