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
DOI:
https://doi.org/10.1090/S0025-5718-97-00832-6
MathSciNet review:
1401944
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be an entire function of positive order and finite type. The subject of this note is the convergence acceleration of polynomial approximants of
by incorporating information about the growth of
for
. We consider ``near polynomial approximation'' on a compact plane set
, which should be thought of as a circle or a real interval. Our aim is to find sequences
of functions which are the product of a polynomial of degree
and an ``easy computable'' second factor and such that
converges essentially faster to
on
than the sequence
of best approximating polynomials of degree
. The resulting method, which we call Reduced Growth method (
-method) is introduced in Section 2. In Section 5, numerical examples of the
-method applied to the complex error function and to Bessel functions are given.
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Additional Information
Jürgen Müller
Affiliation:
Fachbereich IV-Mathematik, Universität Trier, D-54286 Trier, Germany
Email:
jmueller@uni-trier.de
DOI:
https://doi.org/10.1090/S0025-5718-97-00832-6
Received by editor(s):
October 16, 1995
Received by editor(s) in revised form:
April 1, 1996
Article copyright:
© Copyright 1997
American Mathematical Society