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
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