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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Accelerated polynomial approximation
of finite order entire functions
by growth reduction

Author: Jürgen Müller
Journal: Math. Comp. 66 (1997), 743-761
MSC (1991): Primary 65B99; Secondary 30D10
MathSciNet review: 1401944
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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 $f(z)$ for $z\to \infty $. 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 $(f_n)_n$ of functions which are the product of a polynomial of degree $\le n$ and an ``easy computable'' second factor and such that $(f_n)_n$ converges essentially faster to $f$ on $K$ than the sequence $(P_n^*)_n$ of best approximating polynomials of degree $\le n$. 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.

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Jürgen Müller
Affiliation: Fachbereich IV-Mathematik, Universität Trier, D-54286 Trier, Germany

Received by editor(s): October 16, 1995
Received by editor(s) in revised form: April 1, 1996
Article copyright: © Copyright 1997 American Mathematical Society