GEOMETRIC METHODS IN RATIONAL INTERPOLATION THEORY

This paper studies the minimal rational interpolation problem using al gebrogeometric methods. Specifically, we deal in a unified framework w ith the following problems: scalar and matrix interpolation, and left and right tangential interpolation. While the results we prove are kno wn, our methods of proof are quite different. In addition, our proof s hows that these problems can be solved by an application of the Grobne r basis algorithm, a popular computational tool in computer algebra. ( C) Elsevier Science Inc., 1997.