International Congress on Extrapolation and Rational Approximation location:Tenerife, Spain date:January 1992
A general module theoretic framework is used to solve several classical interpolation problems and generalizations thereof in a unified way. These problems are divided into two main families. The first family contains the classical linearized Padé, Padé-Hermite and M-Padé problems and the generalization of the vector M-Padé problem. The second family consists of the Padé problem, the scalar, vector and matrix rational interpolation problems. The solution method is straightforward, recursive and efficient. It can follow any ``path'' in the ``solution table'' even if this ``solution table'' is nonnormal (nonperfect). Reordering of the interpolation data is not required.