Abstract
This paper introduces a method that uses perturbation subspaces for block eigenvector matrices to reduce the modified problem to a sequence of problems of smaller-dimention . These perturbation subspaces are shown to be contained in certain generalized Krylov subspaces of the n-dimentional space, where n is the unbounded dimention of the matrices in the cubic problem . The method converges at least as fast as the corresponding Taylor series, and the convergence can be accelerated further by applying a block generalization of the cubic convergent Rayleigh quptient iteration . Numerical examples are presented to illustrate the applicability of the method .