Embree, MarkSifuentes, Josef A.Soodhalter, Kirk M.Szyld, Daniel B.Xue, Fei2018-06-192018-06-192011-10Embree, Mark, Sifuentes, Josef A., Soodhalter, Kirk M., et al.. "Short-Term Recurrence Krylov Subspace Methods for Nearly-Hermitian Matrices." (2011) <a href="https://hdl.handle.net/1911/102188">https://hdl.handle.net/1911/102188</a>.https://hdl.handle.net/1911/102188The 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.20 ppengTechnical reportTR11-14