Inverse Iteration, Ill-Conditioned Equations and Newton’s Method

@article{Peters1979InverseII,
title={Inverse Iteration, Ill-Conditioned Equations and Newton’s Method},
author={G. Peters and J. H. Wilkinson},
journal={Siam Review},
year={1979},
volume={21},
pages={339-360}
}

Inverse iteration is one of the most widely used algorithms in practical linear algebra but an understanding of its main numerical properties has developed piecemeal over the last thirty years: a major source of misunderstanding is that it requires the solution of very ill-conditioned systems of equations. We describe closely related algorithms which avoid these ill-conditioned systems and explain why the standard inverse iteration algorithm may nevertheless be preferable. The discussion covers… Expand