Continued fraction interpolation

where y_ij=(x_i-x_j)/(y_i-y_j), y_ijk=(x_j-x_k)/(y_ij-y_ik), and y_ijkl=(x_k-x_l)/(y_ijk-y_ijl)….

Algorithm:

(1)   Sort out x’s and y’S in term of x’s in ascending order.

(2)   Calculate y₁,y₁₂,y₁₂₃,y₁₂₃₄,…, and y_1234…n.

(3)   Compute the continued fraction backward.

Attention:

(a)   The same values in y cannot be allowed.

(b)   This method is not for smoothing with errors but for interpolation of points on a function.