The structured distance to normality of Toeplitz matrices with application to preconditioning. (Q2889395)
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scientific article; zbMATH DE number 6043448
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The structured distance to normality of Toeplitz matrices with application to preconditioning. |
scientific article; zbMATH DE number 6043448 |
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7 June 2012
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Toeplitz matrix
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circulant matrix
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nearness problem
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normality
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preconditioning
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Hermitian matrix
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numerical results
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The structured distance to normality of Toeplitz matrices with application to preconditioning. (English)
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An explicit formula for computing the distance in Frobenius norm to a given Toeplitz matrix is presented for generalized Hermitian Toeplitz and particular circulant matrices. The minimization problem for computing the closest \(\{e^{i\varphi }\}\)-circulant matrix is closely related to a minimization problem for finding suitable preconditiers. Some applications where systems with Toeplitz matrices are preconditioned by \(\{e^{i\varphi }\}\)-circulant matrices are presented, theoretical and numerical results provide information on the performance of these preconditioners.
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