关于Arnoldi精化算法的收敛性

对于解大型非对称阵Ａ特征问题的Ａｒｎｏｌｄｉ方法，为克服Ｒｉｔｚ值收敛于特征值时而Ｒｉｔｚ向量不一定收敛于特征向量这一弊病，Ｊｉａ提出了用精化向量了代Ｒｉｔｚ向量的精化算法，并且对于具有相异特征值的Ａ证明了：只要Ｒｉｔｚ值收敛于特征值，精化向量就收敛于特征向量，本文取消对Ａ的限制，证明了即使Ａ可能亏损的一般情形上述结论也成立。

Covergence of refined algorithms on Arnoldi's process for large unsymmetric eigenproblems

For Arnoldi's method to solve large unsymmetric eigenproblems, Jia has proposed that using the refined approximated eigenvectors the refined iterative algorithms can replace Ritz vector in order to surmount that Ritz vectors obtained by Arnoldi's method cannot be guaranteed to conserge in theory even if the Ritz value has proved that if the eigenvalues of A are simple, the refined approximate eigenvectors converge to eigenvectors if Ritz values do. This paper cancles this restriction to A, and shows that the refined iterative algorithms always converge.