Generalized order star theory
In this paper we generalize the theory of order stars of Wanner, Hairer and Nørsett . We show that there is a geometric relation between the location of the zeros and the poles of a rational approximation to the exponential and the distribution of its interpolation points.
By applying this theory we find that the A-acceptability and the general form of the denominator impose bounds on the number and location of the interpolation points. These bounds are used to characterize the A-acceptability properties of various families of rational approximations to exp(x), in particular to verify a conjecture of Ehle  on the order-constrained Chebishev approximations.
Much of the paper is based upon a joint work of the author with M.J.D. Powell .
Unable to display preview. Download preview PDF.
- A. Iserles, Rational interpolation to exp(−x) with application to certain stiff systems, to appear in SIAM J. Num. Anal. Google Scholar
- A. Iserles, Order stars and a saturation theorem for conservation laws, in preparation.Google Scholar
- A. Iserles, M.J.D. Powell, On the A-acceptability of rational approximations to the exponential, DAMTP NA/3, Univ. of Cambridge (1980).Google Scholar