It is well known that for general linear systems, only optimal Krylov methods
with long recurrences exist. For special classes of linear systems it is
possible to find optimal Krylov methods with short recurrences. In this paper
we consider the important class of linear systems with a shifted skew-symmetric
coefficient matrix. We present the MRS3 solver, a minimal residual method that
solves these problems using short vector recurrences. We give an overview of
existing Krylov solvers that can be used to solve these problems, and compare
them with the MRS3 method, both theoretically and by numerical experiments.
From this comparison we argue that the MRS3 solver is the fastest and most
robust of these Krylov method for systems with a shifted skew-symmetric
coefficient matrix.Comment: 23 pages, 3 figure