Journal of computational and applied mathematics vol:33 issue:3 pages:331-346
We generalize our earlier results on rational interpolation which were given in Van Barel and Bultheel (this journal, 1990) for the scalar case and in Bultheel and Van Barel (1990) for the vector case when all the interpolation points coincide, to the case of vector data given at arbitrary points that may coincide or not. This is the vector-valued Newton-Pade problem. We give a recursive algorithm which has the important advantage over other algorithms that overcome a singularity in the interpolation table, not even in the nonnormal vector case. It also generates all the information needed to give all solutions of the problem.