A local restart procedure for iterative projection methods for nonlinear symmetric eigenproblems

For nonlinear eigenvalue problems $T(lambda)x = 0$ satisfying a minmax characterization of its eigenvalues iterative projection methods combined with safeguarded iteration are suitable for computing all eigenvalues in a given interval. Such methods hit their limitation if a large number of eigenvalues (in the interior of the spectrum) are required. In this paper we propose a localized version of safeguarded iteration which is able to cope with this problem.