An implicitly-restarted Krylov subspace method for real symmetric/skew-symmetric eigenproblems

A new implicitly-restarted Krylov subspace method for real symmetric/skew-symmetric generalized eigenvalue problems is presented. The new method improves and generalizes the SHIRA method of Mehrmann and Watkins (2001) [37] to the case where the skew-symmetric matrix is singular. It computes a few eigenvalues and eigenvectors of the matrix pencil close to a given target point. Several applications from control theory are presented and the properties of the new method are illustrated by benchmark examples.