On tangential matrix interpolation

The paper presents an algebraic approach, using polynomial and rational models over an arbitrary field, to tangential interpolation problems, both by polynomial as well as rational matrix functions. Appropriate extensions of scalar problems, associated with the names of Lagrange (first order), Hermite (high order) and Newton (recursive) are derived. The relation of interpolation problems to the matrix Chinese remainder theorem are clarified. Some two sided interpolation problems are discussed, using the theory of tensored functional models.