Re: How to do Chebyshev expansion in Mathematica?

• To: mathgroup at smc.vnet.net
• Subject: [mg68467] Re: [mg68433] How to do Chebyshev expansion in Mathematica?
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sun, 6 Aug 2006 02:56:53 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Needs["Graphics`"];

http://mathworld.wolfram.com/ChebyshevApproximationFormula.html

Clear[ChebyshevApprox];
ChebyshevApprox[n_Integer?Positive,
f_Function, x_]:= Module[{c,xk},
xk=Pi(Range[n]-1/2)/n;
c[j_]= 2*Total[Cos[j*xk]*(f/@Cos[xk])]/n;
Total[Table[c[k]*ChebyshevT[k, x],{k,0,n-1}]]-c[0]/2];

f = 3*#^2*Exp[-2*#]*Sin[2#*Pi]&;

ChebyshevApprox[3,f,x]//Simplify

((-(3/4))*((-E^(2*Sqrt[3]))*(Sqrt[3] - 2*x) - 2*x - Sqrt[3])*x*Sin[Sqrt[3]*Pi])/E^Sqrt[3]

DisplayTogetherArray[
Partition[
Table[
Plot[{f[x],ChebyshevApprox[n,f,x]},{x,-1,1},
Frame->True, Axes->False,
PlotStyle->{Blue,Red},
PlotRange->{-2,10},
Epilog\[Rule]Text["n = " <> ToString[n], {0.25,5}]],
{n,9}],
3],
ImageSize->500];

Bob Hanlon

---- Michael <michael.monkey.in.the.jungle at gmail.com> wrote:
> anybody please give me some pointers? Thanks a lot!
>
>

```

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