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ACCELERATED POLYNOMIAL APPROXIMATION OF FINITE ORDER ENTIRE FUNCTIONS BY GROWTH REDUCTION

By Jürgen Müller

Abstract

Abstract. Let f be an entire function of positive order and finite type. The subject of this note is the convergence acceleration of polynomial approximants of f by incorporating information about the growth of f(z) forz→∞. We consider “near polynomial approximation ” on a compact plane set K, which should be thought of as a circle or a real interval. Our aim is to find sequences (fn)n of functions which are the product of a polynomial of degree ≤ n and an “easy computable ” second factor and such that (fn)n converges essentially faster to f on K than the sequence (P ∗ n)n of best approximating polynomials of degree ≤ n. The resulting method, which we call Reduced Growth method (RG-method) is introduced in Section 2. In Section 5, numerical examples of the RG-method applied to the complex error function and to Bessel functions are given. 1

Year: 2011
OAI identifier: oai:CiteSeerX.psu:10.1.1.192.4592
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