Some new algorithms for the spectral dichotomy methods Original Research Article

Given a regular matrix pencil λB−A having no eigenvalues on the circle Cr of center 0and radius r, we describe a new algorithm to compute iteratively the deflating subspaces ofλB−A corresponding to the eigenvalues inside and outside Cr along with “a spectral condition number” that indicates the numerical quality of the computed deflating subspaces. We then generalize the proposed algorithm to the case where Cr is replaced by a straight line or an ellipse.