Summary

In this paper the accuracy of the rational interpolation by HRFA is discussed. A posteriori error estimate is established by using the near-GCD[8]. Similar results may be obtained for other approximate-GCD algorithms. Until now the accuracy of hybrid rational interpolation, i.e., HRFA, is shown only through numerical examples. Our error estimate and the theorem proposed in this paper give the theoretical relation between HRFA and approximate-GCD algorithms. There remains problems on the HRFA such as

1.

Our numerical experiments show that the algorithm of HRFA works well for smooth elementary functions f(x) [4]. Under what condition does the close zeros of P(x) and Q(x) occur?

2.

How is the HRFA compared to other approximations?