Abstract:

The task of seeking the weak solution (P(X),q(X)) of matrix valued osculatory rational interpolation was converted  into
computing the Groebner bases of R-submodule M of the free module over the polynomial ring. This Groebner bases can be computed recursively to obtain a parametric rational interpolation function with the Groebner bases. Choosing these parameters properly, we may get the desired  matrix valued rational interpolation function.

Key words: matrix valued osculatory rational interpolation, weak interpolation, Groebner base for module