Vector valued rational interpolants over triangular grids

Given in this paper are some results about vector valued rational interpolants over triangular grids by means of Thiele-type branched continued fractions and the Samelson inverse. Characterization theorem and uniqueness theorem in a certain sense are obtained. Moreover, numerical examples are provided to support other properties of vector valued rational interpolants such as boundary interpolation and duality. And it is pointed out that all the results in the vector case can be transplanted to the matrix valued case by the technique of expansion of matrix into vectors.