关于GMRES方法收敛性质的数值实验观测(英文)

SOME OBSERVATIONS ON THE CONVERGENCE BEHAVIOR OF GMRES (Ⅰ)

广义最小剩余法(GMRES)是一种求解线性代数方程组A_x=b的迭代法,对解一类非对称问题特别是由微分方程数值解导出的大型稀疏问题具有相当的竞争力,这里我们报告一些数值试验结果及我们所观察到的收敛性质,在第一部分我们主要讨论GMRES的收敛速度,工作量的大小等,并指出我们所观测到的超线性收敛现象。

The Generalized Minimal (GMRES) method, proposed by Saad and Schultz, is an iterative method for the approximate solution of linear systems of equations Ax=b with A possibly nonsymmetric. It has appeared to be a competitive method for certain classes of problems, specially for many systems which airse after discretization of partial differentialequations. Here we will report on some numerical experiments in which we observed theconvergence behavior and where we tried to trace the effects of Changing the spectral pro-perties of A.