A note on simultaneous preconditioning and symmetrization of non-symmetric linear systems. (Q2889390)
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scientific article; zbMATH DE number 6043443
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on simultaneous preconditioning and symmetrization of non-symmetric linear systems. |
scientific article; zbMATH DE number 6043443 |
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7 June 2012
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iterative method
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sparse matrix
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Lanczos method
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conjugate gradients
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preconditioning
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MINRES
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SYMMLQ
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numerical examples
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A note on simultaneous preconditioning and symmetrization of non-symmetric linear systems. (English)
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The paper describes a technique for simultaneous preconditioning and symmetrization for solving large, sparse and non-symmetric problems by CG, MINRES or SYMMLQ. The approach is based on the theory of self-duality. The paper states that sometimes it is beneficial to replace the original problem \(Ax = b\) with non-symmetric matrix \(A\) by \(A^TMAx = A^TMb\). It is shown how to choose the matrix \(M\) in order to get a good numerical scheme for solving the original problem. The efficiency of the introduced approach is illustrated on several numerical examples. Results are compared on several iterative methods.
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