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MathGroup Archive 2007

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Re: Gauss-Kronrod algorithm

  • To: mathgroup at smc.vnet.net
  • Subject: [mg76943] Re: Gauss-Kronrod algorithm
  • From: acmilan <fanvn_Acmilan at yahoo.com>
  • Date: Wed, 30 May 2007 05:27:54 -0400 (EDT)
  • References: <f04nlc$8kr$1@smc.vnet.net><f1er1h$5g1$1@smc.vnet.net>

Dear Dimitris and Peter,
Thanks so much for your help.
Regards,
Milan
On May 4, 4:31 pm, dimitris <dimmec... at yahoo.com> wrote:
> Hello again.
>
> You should have a look here.
>
> http://reference.wolfram.com/mathematica/tutorial/NIntegrateIntegrati...
>
> 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- Hide quoted text -
>
> - Show quoted text -




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