A new approach to the rational interpolation problem: the vector case

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 we do not need a reordering of the given interpolation data to 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.

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