Embree, MarkSifuentes, Josef A.Soodhalter, Kirk M.Szyld, Daniel B.Xue, Fei2013-07-112013-07-112012Embree, Mark, Sifuentes, Josef A., Soodhalter, Kirk M., et al.. "Short-term Recurrence Krylov Subspace Methods for Nearly Hermitian Matrices." <i>SIAM J. on Matrix Analysis and Applications,</i> 33, no. 2 (2012) Society for Industrial and Applied Mathematics: 480-500. http://dx.doi.org/10.1137/110851006.https://hdl.handle.net/1911/71531The 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.engArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.Journal articleGMRESMINRESnearly Hermitian matriceslow-rank modificationshttp://dx.doi.org/10.1137/110851006