Vector-valued, rational interpolants III
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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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- Vector-valued, rational interpolants III
Volume 2, Issue 1 , pp 263-289
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- Rational interpolation
- Vector-valued data
- Continued fractions