一种改进的利用特征向量的GMRES方法(英文)

An Improved GMRES Method Augmented with Eigenvectors

利用特征向量的重开始的ＧＭＲＥＳ方法是一种解非对称线型系统的，特别是解拥有少量极小特征值的非对称线型系统的有效方法，但应采用的恰当的特征向量数目却很难确定．这将可能导致收敛速度的减慢和数值结果的精度降低．给出了一种改进的利用特征向量的ＧＭＲＥＳ方法，它采用逐次增加特征向量的方法，并可结合特定的收敛准则自适应的确定恰当的特征向量数目．数值结果证明此方法可以得到更高的精度，花费更少的迭代次数和ＣＰＵ时间．

The restarted GMRES method augmented with eigenvectors is a useful method for solving nonsymmetric linear systems, especially the systems with a few of the smallest eigenvalues. But it is difficult to chars the appropriate number of eigenvectors that should be used, so the convergence may be slowed down and the precision could be reduced. This paper presents an improved method which adds the eigenvectors orderly and can be combined with some criterions to decide the proper number of eigenvectors adaptively. The numerical experiments show that this method can give higher precision, less iterates and CPU time.