A geometric view of Krylov subspace methods on singular systems. (Q2889396)
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scientific article; zbMATH DE number 6043449
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A geometric view of Krylov subspace methods on singular systems. |
scientific article; zbMATH DE number 6043449 |
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7 June 2012
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Krylov subspace method
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singular system
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GMRES
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GCR
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least-squares
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algorithms
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two-point boundary value problems
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0.9242787
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0.9108928
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0.89712715
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A geometric view of Krylov subspace methods on singular systems. (English)
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Three Krylov subspace methods, GMRES, restarted GMRES and restarted GCR, are analyzed in their behavior when applied to singular square nonsymmetric systems of linear equations. With an emphasis on geometric aspects, the quantities in the algorithms are decomposed into their components in the range of the coefficient matrix and its orthogonal complement. Extensions, new interpretations and new proofs of previous results of Brown and Walker on when these algorithms yield least-squares solutions and when they break down, i.e., terminate before such a solution is found, are given. The paper concludes with examples of singular systems arising in the discretization of two-point boundary value problems.
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