Dictionary:Newtonian interpolation

{{#category_index:N|Newtonian interpolation}} For a function known at regularly spaced points, y_n=f(x_o+nh), the value at y_u=f(x_o+uh) can be approximated by a series for which the k^th term is u(u–1)...(u–k)Δ^ky_o/k!, where Δ is the forward difference operator. A similar relationship can be used for backward prediction, its k^th term being u(u+1)...(u+k)Δ^ky_o/k!.