A CLASS OF FIRST-ORDER AND 2ND-ORDER INTERPOLATION PROBLEMS IN MODEL-REDUCTION

We consider a class of first- and second-order interpolation problems, and their role in data-driven model reduction. Given a set of M inter polation points, and a first- and second-order datum value for each in terpolation point, we show that a stable rational function may always be fit to these points. Our results generalize those of Mullis and Rob erts, and follow by rephrasing the interpolation problem into one of N evanlinna-Pick type. Connections to the Steiglitz-McBride method of sy stem approximation are also brought out. We establish a sufficient con dition for a fixed point to exist in this iterative approximation meth od, and show that an attractive a priori error bound applies at any su ch fixed point.