Browsing by Author "Soodhalter, Kirk M."

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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.