求解右定两参数特征值问题的精化Jacobi-Davidson方法(英文)

在文献1]中,作者M E Hochstenbach和B Plestenjak认为精化的方法不适合两参数特征值问题,原因是求解两参数特征值问题的精化方法存在着三个问题:即精化Ritz向量收敛性差,运算量大,不能计算多个特征值.本文指出,事实并非如此.针对右定两参数特征值问题,本文提出了一种有效的精化数值方法.并通过理论证明和数值实验说明了Ritz值的收敛性,以及精化Ritz向量具有比通常的Ritz向量更好的收敛性.

Refined Jacobi-Davidson Type Method for a Right Definite Two-Parameter Eigenvalue Problem

In their paper, M E Hochstenbach and B Plestenjak considered that the refined method ~vas not suitable for two-parameter eigenvalue problems because of high costs for computation, poor convergence of refined Ritz vectors and incapacity for computing more than one eigenvalue. In this paper, we show that it is not the case. We propose an efficient refined Jacobi- Davidson type method for a right definite two-parameter eigenvalue problem and show that refined Ritz vectors have better convergence than Ritz vectors and （refined） Ritz values are convergent.