Preconditioners for nondefinite Hermitian Toeplitz systems (Q2706281)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Preconditioners for nondefinite Hermitian Toeplitz systems |
scientific article |
Statements
19 March 2001
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nondefinite Toeplitz matrices
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circulant matrices
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Krylov space methods
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circulant preconditioners
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minimal residual method
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algorithm
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computational complexity
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trigonometric preconditioners
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numerical results
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Preconditioners for nondefinite Hermitian Toeplitz systems (English)
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This paper is concerned with the construction of circulant preconditioners for Toeplitz systems arising from a piecewise continuous generating function with sign changes. NEWLINENEWLINENEWLINEThe authors construct circulant preconditioners for the minimal residual method (MINRES) and prove that for any \(\varepsilon > 0\), only \(O(\log N)\) the singular eigenvalues of the precondioned matrices do not belong to the interval \([1-\varepsilon\), \(1+\varepsilon]\). They construct circulant preconditioners for the case that the generating function of the Toeplitz matrices is not explicitly known. The proposed algorithm has computational complexity of \(O(N \log^2 N)\). The results obtained for the Toeplitz preconditioners are extended for some trigonometric preconditioners in the case of even generating function. NEWLINENEWLINENEWLINESome numerical results from simple test examples are presented.
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