An algorithm similar to Neville's algorithm for constructing the Lagrange interpolating polynomial. Let f(x|x_0, x_1, ..., x_k) be the unique polynomial of kth polynomial order coinciding with f(x) at x_0, ..., x_k. Then f(x|x_0, x_1) | = | 1/(x_1 - x_0) left bracketing bar f_0 | x_0 - x f_1 | x_1 - x right bracketing bar f(x|x_0, x_2) | = | 1/(x_2 - x_0) left bracketing bar f_0 | x_0 - x f_2 | x_2 - x right bracketing bar f(x|x_0, x_1, x_2) | = | 1/(x_2 - x_1) left bracketing bar f(x|x_0, x_1) | x_1 - x f(x|x_0, x_2) | x_2 - x right bracketing bar f(x|x_0, x_1, x_2, x_3) | = | 1/(x_3 - x_2) left bracketing bar f(x|x_0, x_1, x_2) | x_2 - x f(x|x_0, x_1, x_3) | x_3 - x right bracketing bar .