A note on the growth factor in Gaussian elimination for Higham matrices
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2013
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| _version_ | 1866916694858924032 |
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| author | Guo, Qian-Ping Gu, Xian-Ming Li, Hou-biao |
| author_facet | Guo, Qian-Ping Gu, Xian-Ming Li, Hou-biao |
| contents | The Higham matrix is a complex symmetric matrix A=B+iC, where both B and C are real, symmetric and positive definite and $\mathrm{i}=\sqrt{-1}$ is the imaginary unit. For any Higham matrix A, Ikramov et al. showed that the growth factor in Gaussian elimination is less than 3. In this paper, based on the previous results, a new bound of the growth factor is obtained by using the maximum of the condition numbers of matrixes B and C for the generalized Higham matrix A, which strengthens this bound to 2 and proves the Higham's conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1305_5211 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | A note on the growth factor in Gaussian elimination for Higham matrices Guo, Qian-Ping Gu, Xian-Ming Li, Hou-biao Numerical Analysis 15A23, 65F05, 65F35, 65F50 The Higham matrix is a complex symmetric matrix A=B+iC, where both B and C are real, symmetric and positive definite and $\mathrm{i}=\sqrt{-1}$ is the imaginary unit. For any Higham matrix A, Ikramov et al. showed that the growth factor in Gaussian elimination is less than 3. In this paper, based on the previous results, a new bound of the growth factor is obtained by using the maximum of the condition numbers of matrixes B and C for the generalized Higham matrix A, which strengthens this bound to 2 and proves the Higham's conjecture. |
| title | A note on the growth factor in Gaussian elimination for Higham matrices |
| topic | Numerical Analysis 15A23, 65F05, 65F35, 65F50 |
| url | https://arxiv.org/abs/1305.5211 |