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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)  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.doi:10.1016/j.laa.2009.11.009 fatcat:y2o7anqhozdjjbn2r3xkmcnm3q