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Vector-valued, rational interpolants III

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Abstract

In 1963, Wynn proposed a method for rational interpolation of vector-valued quantities given on a set of distinct interpolation points. He used continued fractions, and generalized inverses for the reciprocals of vector-valued quantities. In this paper, we present an axiomatic approach to vector-valued rational interpolation. Uniquely defined interpolants are constructed for vector-valued data so that the components of the resulting vector-valued rational interpolant share a common denominator polynomial. An explicit determinantal formula is given for the denominator polynomial for the cases of (i) vector-valued rational interpolation on distinct real or complex points and (ii) vector-valued Padé approximation. We derive the connection with theε-algorithm of Wynn and Claessens, and we establish a five-term recurrence relation for the denominator polynomials.

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Communicated by Edward B. Saff.

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Graves-Morris, P.R., Jenkins, C.D. Vector-valued, rational interpolants III. Constr. Approx 2, 263–289 (1986). https://doi.org/10.1007/BF01893432

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