Definition
interpolation on top of Chebyshev node
Node
The selection of node can be:
- Chebyshev–Gauss:
- Chebyshev–Lobatto
- etc
Implementation
it can be implemented by Lagrange Interpolation, orthogonal polynomial interpolation, and etc.
OR
import numpy as np
import numpy.linalg as la
n = len(y)
x = np.cos((2 * np.array(list(range(n))) + 1)*np.pi/(2*n))
V = np.zeros((n,n))
V[:,0] = 1
V[:,1] = x
for i in range(2, n):
V[:,i] = 2*x*V[:,i-1] - V[:,i-2]
c = la.solve(V,y)Crude Error
where
- constant
- number of nodes
- the range