Convergence of Polynomial Restart Krylov Methods for Eigenvalue Computation

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dc.contributor.authorBeattie, Christopher A.
dc.contributor.authorEmbree, Mark
dc.contributor.authorSorensen, D.C.
dc.date.accessioned2018-06-18T17:51:07Z
dc.date.available2018-06-18T17:51:07Z
dc.date.issued2003-08
dc.date.noteAugust 2003
dc.description.abstractThe convergence of Krylov subspace eigenvalue algorithms can be robustly measured by the angle the approximating Krylov space makes with a desired invariant subspace. This paper describes a new bound on this angle that handles the complexities introduced by non-Hermitian matrices, yet has a simpler derivation than similar previous bounds. The new bound reveals that ill-conditioning of the desired eigenvalues has little impact on convergence, while instability of unwanted eigenvalues plays an essential role. Practical computations usually require the approximating Krylov space to be restarted for efficiency, whereby the starting vector that generates the subspace is improved via a polynomial filter. Such filters dynamically steer a low-dimensional Krylov space toward a desired invariant subspace. We address the design of these filters, and illustrate with examples the subtleties involved in restarting non-Hermitian iterations.
dc.format.extent21 pp
dc.identifier.citationBeattie, Christopher A., Embree, Mark and Sorensen, D.C.. "Convergence of Polynomial Restart Krylov Methods for Eigenvalue Computation." (2003) <a href="https://hdl.handle.net/1911/102004">https://hdl.handle.net/1911/102004</a>.
dc.identifier.digitalTR03-08
dc.identifier.urihttps://hdl.handle.net/1911/102004
dc.language.isoeng
dc.titleConvergence of Polynomial Restart Krylov Methods for Eigenvalue Computation
dc.typeTechnical report
dc.type.dcmiText
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