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.

翻译：众所周知，对于一般线性系统，仅存在长递推的最优Krylov方法。而对于特殊类型的线性系统，则可能找到具有短递推的最优Krylov方法。本文考虑一类具有移位斜对称系数矩阵的重要线性系统。我们提出MRS3求解器，这是一种利用短向量递推求解此类问题的最小残差方法。本文概述了可用于求解此类问题的现有Krylov求解器，并从理论和数值实验两方面与MRS3方法进行比较。通过对比表明，对于具有移位斜对称系数矩阵的系统，MRS3求解器是这些Krylov方法中速度最快且最稳健的。