Re: Early Results from Mathematica 4.0

*To*: mathgroup at smc.vnet.net*Subject*: [mg18095] Re: Early Results from Mathematica 4.0*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Thu, 17 Jun 1999 12:26:35 -0400*Organization*: Universitaet Leipzig*References*: <7jajk6$k1p@smc.vnet.net> <7jual2$56f@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi, I think the whole idea with Integrate[]/NIntegrate[] of an interpolation function is wrong. Say you have K points x[i], f[i] and you need an expansion in Legendre polynoms with maximum of degree K you can simply create a linear system for the expansion coefficients a[i] y[r_]=Sum[a[i]*LegendereP[i,r],{i,0,K-1}] by the interpolation condition y[x[i]]=f[i]. Mathematica's Fit[] will do a least square approximation when a fewer degree of the expansion is needed. Regards Jens Paul Abbott wrote: > > Kevin J. McCann wrote: > > > I have an > > application in which I take a potential function which is a function of R > > and theta and expand it in terms of Legendre polynomials. To do this I do a > > 2D curve fit on the data and then use NIntegrate to get the Legendre > > coefficients as a function of R. > > I wonder if there is a faster way of doing this computation by > converting the curve fit to an expansion in Legendre polynomials using > symbolic methods and pattern-matching? Perhaps you could post a simple > example of what you are doing. > > Also, you might find that reducing the AccuracyGoal/PrecisionGoal will > make NIntegrate run _much_ faster. > > Cheers, > Paul