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Re: Gauss-Kronrod algorithm
*To*: mathgroup at smc.vnet.net
*Subject*: [mg75538] Re: Gauss-Kronrod algorithm
*From*: dimitris <dimmechan at yahoo.com>
*Date*: Fri, 4 May 2007 04:19:18 -0400 (EDT)
*References*: <f04nlc$8kr$1@smc.vnet.net><f19fuf$4sj$1@smc.vnet.net>
Hello again.
You should have a look here.
http://reference.wolfram.com/mathematica/tutorial/NIntegrateIntegrationRules=2Ehtml
Dimitris
=CF/=C7 dimitris =DD=E3=F1=E1=F8=E5:
> Although this is from the documentation of the upcoming version of
> Mathematica
> I suggest you to have a look!
>
> http://reference.wolfram.com/mathematica/ref/NIntegrate.html
>
> Now let's see some things.
>
> 1) Some useful links
>
> http://en.wikipedia.org/wiki/Gaussian_quadrature
> http://numericalmethods.eng.usf.edu/topics/gauss_quadrature.html
> (amazing site!)
> http://www.sitmo.com/eqcat/13
> http://scholar.google.com/scholar?hl=en&lr=&q=%22Calculation+of+Gau=
ss=
> -Kronrod+Quadrature+Rules%22
> (the first article is of special notice)
>
> 2) Some Mathematica code
>
> In[64]:=
> oo[x_] = Exp[-5*x^4] + (1/2)*x;
>
> In[71]:=
> Integrate[oo[x], {x, -3, 5}]
> {N[%], ({#1, NIntegrate[oo[x], {x, -3, 5}, Method -> #1]} & ) /@
> {Trapezoidal, DoubleExponential, GaussKronrod}}
>
> Out[71]=
> 4 + (8*Gamma[5/4] - Gamma[1/4, 405] - Gamma[1/4, 3125])/(4*5^(1/4))
>
> Out[72]=
> {5.212295737874928, {{Trapezoidal, 5.212295737874928},
> {DoubleExponential, 5.212295737874928},
> {GaussKronrod, 5.212295737874985}}}
>
> In[73]:=
> (ListPlot[Reap[NIntegrate[oo[x], {x, -3, 3}, Method -> #1,
> EvaluationMonitor :> Sow[x]]][[2,1]], PlotLabel -> #1] & ) /@
> {Trapezoidal, DoubleExponential, GaussKronrod};
>
> I hope I help you a bit!
>
> Dimitris
>
>
> =CF/=C7 acmilan =DD=E3=F1=E1=F8=E5:
> > On Apr 24, 3:21 pm, dimitris <dimmec... at yahoo.com> wrote:
> > > Hello.
> > >
> > > As a first hint I suggest you searching in the archives about posts
> > > of V. Antonov of WRI.
> > >
> > > Dimitris
> > >
> > > =CF/=C7 acmilan =DD=E3=F1=E1=F8=E5:
> > >
> > >
> > >
> > > > On Apr 18, 5:16 pm, acmilan <fanvn_Acmi... at yahoo.com> wrote:
> > > > > Dear All,
> > > > > I am looking for the algorithm to calculate the general Gauss-Kro=
nr=
> od
> > > > > points and weights in Mathematica( which is similar with the bui=
lt=
> -in
> > > > > function
> > > > > GaussianQuadratureWeights[n, a, b, prec] for Gauss points and
> > > > > weights)
> > > > > Thank you very much for your help.
> > > > > Best regards,
> > > > > Milan
> > >
> > > > Hi all,
> > > > Anybody helps me on this Mathematica Gauss-Kronrod points and weigh=
ts
> > > > code?
> > > > Thanks and regards,
> > > > Khoi Khoa- Hide quoted text -
> > >
> > > - Show quoted text -
> >
> > Dear Dimitris,
> > I did try to search all the archives but could not find what I want.
> > Do you have any other suggestions?
> > Thanks and regards,
> > Milan
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