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IMA Journal of Mathematical Control and Information 1986 3(2-3):61-88; doi:10.1093/imamci/3.2-3.61
© 1986 by Institute of Mathematics and its Applications
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On the Scalar Rational Interpolation Problem

A. C. ANTOULAS {dagger} and B. D. Q. ANDERSON

Department of Electrical and Computer Engineering, Rice University Houston, Texas 77251–1892, U.S.A. Mathematical System Theory, E.T.H. Zürich CH–8092 Zürich, Switzerland
Department of Systems Engineering, Australian National University Canberra, A.C.T. 2601, Australia

The rational interpolation problem in the scalar case, including multiple points, is solved. In particular a parametrization of all minimal-degree rational functions interpolating given pairs of points is derived. These considerations provide a generalization of the results on the partial realization of linear systems.

{dagger}Most of this research was conducted while the first author was a Visiting Fellow at the Australian National University, August-September 1985. Support was also provided by N.S.F. through Grant ECS-8505293.


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