Thread View: sci.math.num-analysis
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Started by Dan Tyler Abell
Wed, 07 Oct 1992 14:44
numerical integration in several dimensions
Author: Dan Tyler Abell
Date: Wed, 07 Oct 1992 14:44
Date: Wed, 07 Oct 1992 14:44
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I am interested in extensions of Gaussian quadrature to several dimensions (sometimes called "cubature"). Can anyone tell me the current state-of-the-art and/or refer me to appropriate literature? E-mail appreciated. Thanks in advance.
Re: numerical integration in several dimensions
Author: Herman Rubin
Date: Thu, 08 Oct 1992 01:08
Date: Thu, 08 Oct 1992 01:08
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In article <1992Oct7.144450.5760@wam.umd.edu> dabell@quark.umd.edu writes:
>I am interested in extensions of Gaussian quadrature to several
>dimensions (sometimes called "cubature"). Can anyone tell me
>the current state-of-the-art and/or refer me to appropriate
>literature? E-mail appreciated. Thanks in advance.
There are results of this type, but not particularly new, and the
real problem is that unless LOTS of function evaluations are done,
they do not get into the asymptotics.
It is not necessarily the case that even in one dimension, Gaussian
quadrature is that great. If one uses 32-point quadrature, the result
is exact for polynomials of degree 63, but it is not too hard to find
"natural" functions which are not well approximated by polynomials of
degrees under the thousands, at least.
--
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@snap.stat.purdue.edu (Internet, bitnet)
{purdue,pur-ee}!snap.stat!hrubin(UUCP)
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