Convergence Acceleration Applied to Sinc Approximation with Application to Approximation of |χ|^a

Abstract

In this paper we shall study the role of Chebyshev acceleration [4] on Sinc approximation [9]. When used properly, n—point Sinc approximants con-verge at the O(e ^-cn1/2) rate. Whereas this rate of convergence is often close to optimal [1], extrema.l functions which belong to the Hardy optimality space, H^p(D)={f∈ Hol(D):∥f∥ _p < ∞}, with 1 < p < ∞ which cannot be continued analytically into a larger domain D’ are rarely known in applications. Hence it follows, that for nearly all f encountered in applications, there exists a family of functions Hr(D’) with D C D’ such that the Sinc approximations associated with ’D’ converge more rapidly for our particular function f than the corresponding ones for D. It follows, as a consequence, that Chebyshev acceleration can nearly always be applied to improve the accuracy of Sinc approximation.