Short-term Recurrence Krylov Subspace Methods for Nearly Hermitian Matrices
Sifuentes, Josef A.
Soodhalter, Kirk M.
Szyld, Daniel B.
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.
GMRES; MINRES; nearly Hermitian matrices; low-rank modifications