Inverse iteration on defective matrices
Nai Fu Chen · Mathematics of Computation · 1977
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 × 2 2 \times 2 example, and a sufficient condition for the convergence of the vector sequence is given.