Riemannian trust-region methods for H2 optimal model reduction

In this paper, the Riemannian trust-region method for the H
²
optimal model reduction problem is proposed. The problem is regarded as optimization problems on the Stiefel and Grassmann manifolds and several geometric quantities of the problems are discussed to develop the Riemannian trust-region method. Numerical experiments show that the proposed methods can solve the H
²
optimal model reduction problem effectively.