Article View: sci.math.num-analysis
Article #593Re: numerical integration in several dimensions
From: Herman Rubin
Date: Thu, 08 Oct 1992 01:08
Date: Thu, 08 Oct 1992 01:08
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1487 bytes
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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<1992Oct7.144450.5760@wam.umd.edu>Show Full Headers
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Path: arc1-ca.pugleaf.net!sparky!uunet!cis.ohio-state.edu!zaphod.mps.ohio-state.edu!sample.eng.ohio-state.edu!purdue!mentor.cc.purdue.edu!hrubin From: hrubin@mentor.cc.purdue.edu (Herman Rubin) Newsgroups: sci.math.num-analysis Subject: Re: numerical integration in several dimensions Message-ID: <Bvs362.4wo@mentor.cc.purdue.edu> Date: 8 Oct 92 01:08:22 GMT References: <1992Oct7.144450.5760@wam.umd.edu> Organization: Purdue University Statistics Department Lines: 20