LagrangeAlgorithm.txt

Given n points (X_0), Y_0) ... (X_n, Y_n)
We consider this a tabulation of function values Y_i = f(X_i)
X_i < X_i+1

Compute coefficients  C_i  i=0..r such that
the function  g(X) = C_n X^n + C_n-1 X^n-1 + ... + C_1 X + C_0
all Y_i-g(X_i) =0, is a Lagrange Fit of the points.

Algorithm:
Find g(X) = sum k=0 to n f(X) L_n,k(x)
for discrete points
Find g(X) = sum k=0 to n Y_k L_n,k(X)
Collect C_i from sum of polynomials

L_n,k(X) is nth Lagrange Polynomial at point k.
L_n,k(X) = product i=0 to n (X - X_i)/(X_k - X_i) 

See "Evaluate" and "Integrate" for the uses of the coefficients.