Chebyshev points¶

Chebyshev points are defined in the interval $[-1,+1]$. They are obtained as projections of uniformly spaced points on the unit circle onto the $x$-axis. For any $N \ge 2$ they are defined as follows $$ \theta_i = \frac{\pi i}{N-1}, \qquad x_i = \cos(\theta_i), \qquad i=0,1,\ldots,N-1 $$

In [31]:

from numpy import pi,linspace,cos,sin
from matplotlib.pyplot import plot,axis

In [34]:

t = linspace(0,pi,1000)
xx = cos(t)
yy = sin(t)
plot(xx,yy)

N = 10
theta = linspace(0,pi,N)
plot(cos(theta),sin(theta),'o')
for i in range(N):
    x1 = [cos(theta[i]), cos(theta[i])]
    y1 = [0.0, sin(theta[i])]
    plot(x1,y1,'k--',cos(theta[i]),0,'sr')
axis([-1.1, 1.1, 0.0, 1.1])
axis('equal')

Out[34]:

(-1.0, 1.0, 0.0, 1.0)