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