(*						      *)
(* Numerical Mathematics and Computing, Fifth Edition *)
(* Ward Cheney & David Kincaid		              *)
(* Brooks/Cole Publ. Co.			      *)
(* (c) 2003                                           *)
(* No warranties implied or expressed.	              *)
(* File: runge_fcn				      *)

(* polynomial interpolation: Runge function  - equal spacing*)
F[x_]:=1/(1 + x*x)
a=-5; b=5; n=8; h=(b-a)/n;
data = Table[N[{x,F[x]}], {x, a, b, h}]
plotdata = ListPlot[data]
Fit[data, Table[x^i, {i,0,n}],x]
plotcurve=Plot[%,{x,a,b}]
Show[plotdata, plotcurve]

(* polynomial interpolation: Runge function - Chebyshev spacing*)
F[x_]:=1/(1 + x*x)
a=-5; b=5; n=8; h=(b-a)/n;
data = Table[N[{0.5*((a+b)+(b-a)*Cos[(i/n)*Pi]),
               F[0.5*((a+b)+(b-a)*Cos[(i/n)*Pi])], 
               {1, 0, n}]
plotdata = ListPlot[data]
Fit[data, Table[x^i, {i,0,n}],x]
plotcurve=Plot[%,{x,a,b}]
Show[plotdata, plotcurve]