New results on relationships between multipoint Padé approximation and stability preserving methods in model reduction

Three well-known stability preserving methods of reduction are shown to be special forms of the multipoint pade approximation. Two of the methods—the modified forms of the Schwarz approximation and the stability equation method—are consequently shown to be closely related. Previously observed properties of the methods are explained by treating them as multipoint approximants, and the significance of using expansion points on the imaginary axis is shown to be central to stability preservation.