Krylov sequences of maximal length and convergence of GMRES (Q1279690)
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scientific article; zbMATH DE number 1251182
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Krylov sequences of maximal length and convergence of GMRES |
scientific article; zbMATH DE number 1251182 |
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Krylov sequences of maximal length and convergence of GMRES (English)
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6 July 1999
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A complete parametrization is given for the set of all pairs \((A,b)\) for which \(\text{GMRES}(A,b)\) generates the prescribed convergence curve while matrix \(A\) has a prescribed set of eigenvalues. Moreover, a characterization of the right-hand sides \(b\) for which the \(\text{GMRES}(A, B)\) converges exactly in \(m\) steps, where \(m\) is the given degree of the minimal polynomial of \(A\).
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Krylov sequences
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minimal polynomial
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GMRES method
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convergence
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generalized minimal residual method
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eigenvalues
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