Convergence behavior of the Schur recursion in the Krein space for the J-spectral factorization

We present a "Krein-space version" of the Schur recursion for the J-spectral factorization which arises in H^∞-related problems. The most notable difference of the proposed Schur recursion from the ordinary one is that the proposed recursion can handle temporary changes of the inertia during the process. We show that the Schur recursion in the Krein-space converges to a J-spectral factor exponentially under a suitable condition.