The Stability of GMRES Convergence, with Application to Approximate Deflation Preconditioning

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dc.contributor.authorSifuentes, Josef A.
dc.contributor.authorEmbree, Mark
dc.contributor.authorMorgan, Ronald B.
dc.date.accessioned2018-06-19T17:46:43Z
dc.date.available2018-06-19T17:46:43Z
dc.date.issued2011-09
dc.date.noteSeptember 2011
dc.description.abstractHow does GMRES convergence change when the coefficient matrix is perturbed? Using spectral perturbation theory and resolvent estimates, we develop simple, general bounds that quantify the lag in convergence such a perturbation can induce. This analysis is particularly relevant to preconditioned systems, where an ideal preconditioner is only approximately applied in practical computations. To illustrate the utility of this approach, we combine our analysis with Stewart's invariant subspace perturbation theory to develop rigorous bounds on the performance of approximate deflation preconditioning using Ritz vectors.
dc.format.extent21 pp
dc.identifier.citationSifuentes, Josef A., Embree, Mark and Morgan, Ronald B.. "The Stability of GMRES Convergence, with Application to Approximate Deflation Preconditioning." (2011) <a href="https://hdl.handle.net/1911/102187">https://hdl.handle.net/1911/102187</a>.
dc.identifier.digitalTR11-13
dc.identifier.urihttps://hdl.handle.net/1911/102187
dc.language.isoeng
dc.titleThe Stability of GMRES Convergence, with Application to Approximate Deflation Preconditioning
dc.typeTechnical report
dc.type.dcmiText
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