INVERSE ITERATION ON DEFECTIVE MATRICES

Very often, inverse iteration is used with shifts to accelerate convergence to an eigenvector. In this paper, it is shown that, if the eigenvalue belongs to a nonlinear elementary divisor, the vector sequences may diverge even when the shift sequences converge to the eigenvalue. The local behavior is discussed through a 2 x 2 example, and a sufficient condition for the convergence of the vector sequence is given.