On the A -Acceptability of Rational Approximations that Interpolate the Exponential Function
Arieh Iserles, M. J. D. Powell · IMA Journal of Numerical Analysis · 1981
Rational approximations to exp (x), which use all the available coefficients to satisfy interpolation conditions (which may be Hermitian) are considered. It is shown that the only A-acceptable approximations of this kind are the functions of Ehle & Picel (1975) and Norsett (1975). These results are used to verify a conjecture of Ehle (1976) on the characterization of the A-acceptable order-constrained Chebyshev approximations to exp (x).