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• W1984263725 endingPage "1109" @default.
• W1984263725 startingPage "1074" @default.
• W1984263725 abstract "The performance of Krylov subspace eigenvalue algorithms for large matrices can be measured by the angle between a desired invariant subspace and the Krylov subspace. We develop general bounds for this convergence that include the effects of polynomial restarting and impose no restrictions concerning the diagonalizability of the matrix or its degree of nonnormality. Associated with a desired set of eigenvalues is a maximum reachable invariant subspace that can be developed from the given starting vector. Convergence for this distinguished subspace is bounded in terms involving a polynomial approximation problem. Elementary results from potential theory lead to convergence rate estimates and suggest restarting strategies based on optimal approximation points (e.g., Leja or Chebyshev points); exact shifts are evaluated within this framework. Computational examples illustrate the utility of these results. Origins of superlinear effects are also described." @default.
• W1984263725 created "2016-06-24" @default.
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• W1984263725 date "2004-01-01" @default.
• W1984263725 modified "2023-10-16" @default.
• W1984263725 title "Convergence of Restarted Krylov Subspaces to Invariant Subspaces" @default.
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• W1984263725 doi "https://doi.org/10.1137/s0895479801398608" @default.
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