Rational Interpolation Methods for Symmetric Sylvester Equations
Peter Benner, Tobias Breiten · MPG.PuRe (Max Planck Society) · 2014
We discuss low-rank approximation methods for large-scale symmetric Sylvester equations.Following similar discussions for the Lyapunov case, we introduce an energy norm by the symmetric Sylvester operator.Given a rank nr, we derive necessary conditions for an approximation being optimal with respect to this norm.We show that the norm minimization problem is related to an objective function based on the H 2 -inner product for symmetric state space systems.This objective function leads to first-order optimality conditions that are equivalent to the ones for the norm minimization problem.We further propose an iterative procedure and demonstrate its efficiency by means of some numerical examples.