The Compass (Star) Identity for Vector-valued Rational Interpolants
Peter R.\ Graves--Morris, Bernhard Beckermann
Publication ANO 355, submitted

The compass identity (Wynn's five point star identity) for Padé approximants connects neighbouring elements called N, S, E, W and C in the Padé table. Its form has been extended to the cases of rational interpolation of ordinary (scalar) data and iterpolation of vector--valued data. In this paper, full specification of the associated five point identity for the scalar denominator polynomials and the vector numerator polynomials of the vector--valued rational interpolants are given, as well as the related generalisations of Froebenius' identities. Unique minimal forms of the polynomials constituting the interpolants and results about unattainable points correspond closely to their counterparts in the scalar case.

This work was supported in part by the EC--HCM project ROLLS under contract CHRX-C793-0416.