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| Natura: | Preprint |
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2018
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| Accesso online: | https://arxiv.org/abs/1810.12720 |
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| _version_ | 1866916161510178816 |
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| author | Hari, Vjeran Begovic, Erna |
| author_facet | Hari, Vjeran Begovic, Erna |
| contents | In this paper we prove the global convergence of the complex Jacobi method for Hermitian matrices for a large class of generalized serial pivot strategies. For a given Hermitian matrix $A$ of order $n$ we find a constant $γ<1$ depending on $n$, such that $S(A')\leqγ{S(A)}$, where $A'$ is obtained from $A$ by applying one or more cycles of the Jacobi method and $S(\cdot)$ stands for the off-norm. Using the theory of complex Jacobi operators, the result is generalized so it can be used for proving convergence of more general Jacobi-type processes. In particular, we use it to prove the global convergence of Cholesky-Jacobi method for solving the positive definite generalized eigenvalue problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1810_12720 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On the convergence of complex Jacobi methods Hari, Vjeran Begovic, Erna Numerical Analysis 65F15 In this paper we prove the global convergence of the complex Jacobi method for Hermitian matrices for a large class of generalized serial pivot strategies. For a given Hermitian matrix $A$ of order $n$ we find a constant $γ<1$ depending on $n$, such that $S(A')\leqγ{S(A)}$, where $A'$ is obtained from $A$ by applying one or more cycles of the Jacobi method and $S(\cdot)$ stands for the off-norm. Using the theory of complex Jacobi operators, the result is generalized so it can be used for proving convergence of more general Jacobi-type processes. In particular, we use it to prove the global convergence of Cholesky-Jacobi method for solving the positive definite generalized eigenvalue problem. |
| title | On the convergence of complex Jacobi methods |
| topic | Numerical Analysis 65F15 |
| url | https://arxiv.org/abs/1810.12720 |