Re: Gauss-Kronrod algorithm
- To: mathgroup at smc.vnet.net
- Subject: [mg75468] Re: Gauss-Kronrod algorithm
- From: dimitris <dimmechan at yahoo.com>
- Date: Wed, 2 May 2007 03:48:34 -0400 (EDT)
- References: <f04nlc$8kr$1@smc.vnet.net><f16pjl$70u$1@smc.vnet.net>
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+Gauss= -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-Kronr= od > > > > points and weights in Mathematica( which is similar with the built= -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 weights > > > 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