Article View: sci.math.num-analysis
Article #463Re: Oscillatory Integration?
From: Joseph Mathew
Date: Sat, 05 Sep 1992 02:19
Date: Sat, 05 Sep 1992 02:19
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1465 bytes
In article <92247.091826J0S@psuvm.psu.edu> J0S@psuvm.psu.edu (Jack W. Sharer) writes: >I'm having to evaluate this integral: > > /\ 0.5 > / N > / f(x) D (2 pi x + phi) dx > / > \/ -0.5 > > N >for N ~ 500 and where D (x) is the N-point Dirichlet kernel: > > > iNx > N e - 1 > D (x) = --------, i = sqrt(-1) (highly oscilatory for large N) > ix > e - 1 > >I'm successfully using a 2000-point Simpson integration, but I cannot >begin to evaluate all the needed cases (limited by computer resources). > >Could you suggest a change of variable or another technique which >would dramatically improve the integration speed? Since D(x;N) = 1 + exp(ix) + exp(2ix) + ... + exp((N-1)ix) aren't you just looking for the sum of the Fourier coefficients? Joseph Mathew
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<1992Sep5.021942.29986@eagle.lerc.nasa.gov>Path:
arc1-ca.pugleaf.net!sparky!uunet!zaphod.mps.ohio-state.edu!magnus.acs.ohio-state.edu!usenet.ins.cwru.edu!eagle!steelhead.lerc.nasa.gov!fsjmReferences:
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Newsgroups: sci.math.num-analysis Path: arc1-ca.pugleaf.net!sparky!uunet!zaphod.mps.ohio-state.edu!magnus.acs.ohio-state.edu!usenet.ins.cwru.edu!eagle!steelhead.lerc.nasa.gov!fsjm From: fsjm@steelhead.lerc.nasa.gov (Joseph Mathew) Subject: Re: Oscillatory Integration? Message-ID: <1992Sep5.021942.29986@eagle.lerc.nasa.gov> Sender: fsjm@bart.lerc.nasa.gov Nntp-Posting-Host: steelhead.lerc.nasa.gov Organization: NASA Lewis Research Center [Cleveland, Ohio] References: <92247.091826J0S@psuvm.psu.edu> Date: Sat, 5 Sep 1992 02:19:42 GMT Lines: 30