On the relation between the continued fraction expansion and moments matching methods of model reduction †

Abstract
A widely used form of transfer function model is $ Two methods of approximating such transfer function models by lower order models, the continued fraction expansion of Chen and Shieh and the moments matching method of Gibilaro and Lees, are compared. It is demonstrated that these two methods can give identical results. An efficient computational procedure for the moments matching method is described and the results of computation for the reduction of a seventh-order model are given.