Duality in vector Padé-Hermite approximation problems

The article defines a class of dual vector Padé-Hermite problems. It describes dual basis matrices for the solution spaces of such problems and proves their properties. We show how degree restrictions can be imposed on vector Padé-Hermite problems and what the effect is on the dual basis matrices. o show that the classical duality between Padé-Hermite problems of type I and type II is a special case of vector Padé-Hermite duality. This is proved without the classical restrictive assumption of normality. ticle proposes an algorithm that solves two dual vector Padé-Hermite problems at the same time, returning dual basis matrices of the respective solution spaces.