Geometric methods in rational interpolation theory Original Research Article

This paper studies the minimal rational interpolation problem using algebrogeometric methods. Specifically, we deal in a unified framework with the following problems: scalar and matrix interpolation, and left and right tangential interpolation. While the results we prove are known, our methods of proof are quite different. In addition, our proof shows that these problems can be solved by an application of the Gröbner basis algorithm, a popular computational tool in computer algebra.