A general minimal residual Krylov subspace method for large-scale model reduction

This paper considers approximating a given nth-order stable transfer matrix G(s) by an rth-order stable transfer matrix G_r(s) in which n≫r, and where n is large. The Arnoldi process is used to generate a basis to a part of the controllability subspace associated with the realization of G(s), and a residual error is defined for any approximation in this subspace. We establish that minimizing the L_∞ norm of this residual error over the set of stable approximations leads to a 2-block distance problem. Finally, the solution of this distance problem is used to construct reduced-order approximate models. The behavior of the algorithms is illustrated with a simple example