The effects of inexact solvers in algorithms for symmetric eigenvalue problems

This paper analyses the effects of inaccurate linear solvers on the behaviour of inverse iteration and Rayleigh quotient iteration. We derive an expression for the worst-case perturbation of the convergence factor of the exact iteration, due to the inexact solution. A necessary and sufficient condition on the approximate eigenvector for the improvement of the next iterate follows from that formula. Preceding this, several new inequalities describe the relation between the errors in the approximate eigenvector, the approximate eigenvalue and the corresponding residual.