author: Jia, Zhongxiao
shorttitle: Improving eigenvectors
source: J. Comput. Maath. 18, No. 3, 265-276 (2000)
rsclass: 65F10; 65K05
keywords: Arnoldi method, eigenvectors, large unsymmetric matrices
revtext: The usual m-step Arnoldi method (searching for r eigenvalues and eigenvectors of a large unsymmetric matrix or operator A in the m-dimensional Krylov basis) does not usually make an explicit use of the (available) (m+1)-st Krylov state. The key idea of the authors is that its knowledge could improve the quality of the eigenvectors cheaply. They test the corresponding (residual minimization) modification of the algorithm and illustrate their gains numerically. Using, typically, r = 3 and m from 30 till 80 they achieve a visible (a few units) saving in dimension m measured in terms of the restarts and/or in the number of matrix-vector multiplications.