that n is fixed. Among all possible
choices for Q(x) and thus among all possible
choices for the distinct nodes in [-1,1],
the polynomial is the unique choice which has the property
Proof Chebyshev Polynomials Chebyshev Polynomials
Exploration for the
theorem. Construct Q(x) of degree n using the
n+1 Chebyshev nodes and compare it to
Construct Q(x) of degree n using the n+1 Chebyshev nodes and compare it to .
Case (i). Using 2 nodes.
Case (ii). Using 3 nodes.
Case (iii). Using 4 nodes.
The symbolic manipulation required to simplify the above polynomial is overwhelming. However we can simplify the list of coefficients.
(c) John H. Mathews 2004