Efficient and stable Arnoldi restarts for matrix functions based on quadrature (Q2923364)
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scientific article; zbMATH DE number 6356191
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Efficient and stable Arnoldi restarts for matrix functions based on quadrature |
scientific article; zbMATH DE number 6356191 |
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15 October 2014
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matrix function
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integral expression of the error
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Gaussian quadrature
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restart
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Krylov subspace approximation
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restarted Arnoldi method
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restarted Lanczos method
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deflated restarting
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polynomial interpolation
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Padé approximation
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numerical test
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0.9038173
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0.8823811
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0.8759383
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0.8750809
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0.8706089
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0.8654986
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0.86534363
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Efficient and stable Arnoldi restarts for matrix functions based on quadrature (English)
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This paper deals with the computation of \(f(A)b\), the action of a matrix function on a vector. An integral representation is presented for the error of the iterates in the Arnoldi method. Then an quadrature-based restarting Arnoldi algorithm is derived. This new method is applicable for a large class of functions, requires no a priori spectral information, and runs with essentially constant computational work per restart cycle. Numerical tests are presented to show the efficiency and numerical stability of the proposed method.
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