We show how the error of HRFA satisfies the error estimate
(11).
As a practical example, a data set

is considered and approximated by HRFA with the accuracy level .

The data set *D*
is obtained by discretization of a function
*f*(*x*)=1/(1+25*x*^{2}).
Because of the presence of a roundoff error,
rational interpolation of *D* is obtained by linearized equations such as

The leading and the second coefficients of

near-GCD(

Thus rational function is obtained by (8) as

The expression can be replaced by

The result satisfies the theorem 4.1.

IMACS ACA'98 Electronic Proceedings