Browsing by Author "Sifuentes, Josef A."

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    Short-term Recurrence Krylov Subspace Methods for Nearly Hermitian Matrices
    (Society for Industrial and Applied Mathematics, 2012) Embree, Mark; Sifuentes, Josef A.; Soodhalter, Kirk M.; Szyld, Daniel B.; Xue, Fei
    The progressive GMRES algorithm, introduced by Beckermann and Reichel in 2008, is a residual-minimizing short-recurrence Krylov subspace method for solving a linear system in which the coefficient matrix has a low-rank skew-Hermitian part. We analyze this algorithm, observing a critical instability that makes the method unsuitable for some problems. To work around this issue we introduce a different short-term recurrence method based on Krylov subspaces for such matrices, which can be used as either a solver or a preconditioner. Numerical experiments compare this method to alternative algorithms.
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    Short-Term Recurrence Krylov Subspace Methods for Nearly-Hermitian Matrices
    (2011-10) Embree, Mark; Sifuentes, Josef A.; Soodhalter, Kirk M.; Szyld, Daniel B.; Xue, Fei
    The Progressive GMRES algorithm, introduced by Beckermann and Reichel in 2008, is a residual-minimizing short-recurrence Krylov subspace method for solving a linear system in which the coefficient matrix has a low-rank skew-Hermitian part. We analyze this algorithm, observing a critical instability that makes the method unsuitable for some problems. To work around this issue we introduce a different short-term recurrence method based on Krylov subspaces for such matrices, which can be used as either a solver or a preconditioner. Numerical experiments compare this method to alternative algorithms.
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    The Stability of GMRES Convergence, with Application to Approximate Deflation Preconditioning
    (2011-09) Sifuentes, Josef A.; Embree, Mark; Morgan, Ronald B.
    How 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.