#
# Numerical Mathematics and Computing, Fifth Edition
# Ward Cheney & David Kincaid
# Brooks/Cole Publ. Co.
# (c) 2003
#
# file:  runge_fun
#
# This is the degree-8 interpolating polynomial for 1/(1+x^2)
# on the interval [-5,5], using chebyshev nodes.

with(linalg):
x := evalf(vector(9, i-> 5.0*cos((i-1)*Pi/8.0))):
y := evalf(vector(9, i->(1.0+x[i]^2)^(-1))):
f := interp(x,y,t):
plot1 := plot(f, t=-5..5):
l := [[x[n], y[n]] $n=1..9];
plot2 := plot(l, t=-5..5, style = point, symbol= diamond, thickness = 3);
plots [display]({plot1,plot2});