New convergence bounds are presented for weighted, preconditioned, and deflated GMRES for the solution of large, sparse, nonsymmetric linear systems, where it is assumed that the symmetric part of the coefficient matrix is positive definite. The new bounds are sufficiently explicit to indicate how to choose the preconditioner and the deflation space to accelerate the convergence. One such choice of deflating space is presented, and numerical experiments illustrate the effectiveness of such space.

翻译：针对系数矩阵对称部分正定的大规模稀疏非对称线性系统，本文提出了加权、预处理及消阶GMRES方法的新收敛界。这些新界值具有充分的显式形式，能够指导预处理矩阵与消阶空间的选择以加速收敛。本文给出了一种消阶空间的具体选取方案，并通过数值实验验证了该空间的有效性。