From: Art Werschulz <agw@smolyak.cs.columbia.edu>
Subject: Re: Gauss Integration
Date: 31 May 2001 21:45:00 -0400
Newsgroups: sci.math.num-analysis
Summary: Gauss quadrature optimal for numerical integration of analytic functions?

Hi.

wng@uiuc.edu writes:

> I'm just curious about why you need an order >15 Legendre polynomial
> for your integration.  If the integral is oscillatory, you may have
> to partition the integral into sections, each containing a period of
> the oscillation and then use a lower order polynomial.  An order >15
> does sound a little excessive.

Gauss integration (and variants thereof) is optimal for integrating
certain classes of analytic integrands.  The higher the accuracy
desired, the higher one should choose the order of the Gauss
integration scheme. 

For the gory details, see:

M. A. Kowalski, H. Wozniakowski, A. G. Werschulz,
``Is Gauss quadrature optimal for analytic functions?''
Numerische Mathematik, Vol. 47, pp. 89--98, 1985.

-- 
Art Werschulz (8-{)}   "Metaphors be with you."  -- bumper sticker
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Internet: agw@cs.columbia.edu<a href="http://www.cs.columbia.edu/~agw/">WWW</a>
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