The compass (star) identity for vector-valued rational interpolants
The compass identity, also known as Wynn's five point star identity, connects five neighbouring elements in the Padé table: a central element and its four immediate neighbours in the main compass directions. Such a relation has been generalized to vector-valued rational interpolants [\textit{P. R. Graves-Morris} and \textit{C. D. Jenkins}, Vector valued rational interpolants III, Constructive Approximation 2, 263-289 (1986; Zbl 0614.41016)]. The original proof makes use of five-point relations connecting the scalar denominators and the vector-valued numerators separately. In this paper, another derivation of the latter identities is given. The proof is based on generalizations of classical Frobenius identities. Conclusions about minimality of the degrees in numerator and denominator representing the approximants and results about unattainable points are also given.
scientific article; zbMATH DE number 1083927