Polynomial problems.

*To*: mathgroup at smc.vnet.net*Subject*: [mg4232] Polynomial problems.*From*: f85-tno at mimas.nada.kth.se (Tommy Nordgren)*Date*: Tue, 18 Jun 1996 03:28:48 -0400*Organization*: Royal Institute of Technology, Stockholm, Sweden*Sender*: owner-wri-mathgroup at wolfram.com

I have a set of orthogonal polynomials in x,y,z, which is Gram-Scmidt orthogonalized with respect to integration over the unit sphere. 1. How can I generate a C function to compute my polynomials? (Prototype double mypoly(double x,double y, double z,int index)). 2. How can I find a set of sampling points and weights to compute the scalar products with respect to a function I wan't to approximate. I'm seeking an optimal set of points. 3. The scalar product used is computationally very expensive. Is there any way to optimize the Gram-Smidt orthogonalization operator, to allow computing higher order polynomials in a reasonable time. (Scalar product is similar to this two-dimensional example: Integrate[(#1 #2)/.{x->r Cos[fi], y-> r Sin[fi]}*r,{r,0,1},{fi,0,2Pi}]&) -- ------------------------------------------------------------------------- Tommy Nordgren "Home is not where you are born, Royal Institute of Technology but where your heart finds peace." Stockholm Tommy Nordgren - The dying old crone f85-tno at nada.kth.se -------------------------------------------------------------------------- ==== [MESSAGE SEPARATOR] ====