A new formal approach to the rational interpolation problem

Summary An elegant and fast recursive algorithm is developed to solve the rational interpolation problem in a complementary way compared to existing methods. We allow confluent interpolation points, poles, and infinity as one of the interpolation points. Not only one specific solution is given but a nice parametrization of all solutions. We also give a linear algebra interpretation of the problem showing that our algorithm can also be used to handle a specific class of structured matrices.