Constructive Approximation

, Volume 2, Issue 1, pp 263–289

Vector-valued, rational interpolants III

  • P. R. Graves-Morris
  • C. D. Jenkins


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.

AMS classification


Key words and phrases

Rational interpolation Vector-valued data Continued fractions 


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Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • P. R. Graves-Morris
    • 1
  • C. D. Jenkins
    • 1
  1. 1.Mathematical InstituteUniversity of KentCanterburyEngland

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