Abstract: A new algorithm was derived for determining a parameterization of multivariate osculatory rational functions a(X)/b(X) interpolating an arbitrary sequence of points by means of Groebner bases of submodules of the free module over the polynomial ring in multivariate variable. For Cauchy multivariate rational interpolation, the algorithm is a Newton algorithm.

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