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.
The preconditioned iterative solvers for solving Sylvester tensor equations are considered in this paper.By fully exploiting the structure of the tensor equation,we propose a projection method based on the tensor format,which needs less flops and storage than the standard projection method.The structure of the coefficient matrices of the tensor equation is used to design the nearest Kronecker product(NKP) preconditioner,which is easy to construct and is able to accelerate the convergence of the iterative solver.Numerical experiments are presented to show good performance of the approaches.
