Initializing iterative projection methods for rational symmetric eigenproblems

Abstract

In this paper we consider sparse, symmetric eigenproblems which are rational perturbations of small rank of linear eigenproblems. Problems of this type arise in structural dynamics and in vibrations of fluid-solid structures. Taking advantage of the limit behaviour of certain parameter dependent linear eigenproblems we construct a suitable initial basis for iterative projection methods of Jacobi-Davidson or Arnoldi type.