A Generalized Eigenvalue Approach for Solving Riccati Equations
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TL;DR
A numerically stable algorithm is derived to compute orthonormal bases for any deflating subspace of a regular pencil $\lambda B - A$ based on an update of the QZ-algorithm, in order to obtain any desired ordering of eigenvalues in the quasitriangular forms constructed by this algorithm.
Abstract
A numerically stable algorithm is derived to compute orthonormal bases for any deflating subspace of a regular pencil $\lambda B - A$. The method is based on an update of the $QZ$-algorithm, in order to obtain any desired ordering of eigenvalues in the quasitriangular forms constructed by this algorithm. As applications we discuss a new approach to solve Riccati equations arising in linear system theory. The computation of deflating subspaces with specified spectrum is shown to be of crucial importance here.