The divided difference f[x_0, x_1, x_2, ..., x_n], sometimes also denoted [x_0, x_1, x_2, ..., x_n], on n + 1 points x_0, x_1, ..., x_n of a function f(x) is defined by f[x_0] congruent f(x_0) and f[x_0, x_1, ..., x_n] = (f[x_0, ..., x_(n - 1)] - f[x_1, ..., x_n])/(x_0 - x_n) for n>=1. The first few differences are f[x_0, x_1] | = | (f_0 - f_1)/(x_0 - x_1) f[x_0, x_1, x_2] | = | (f[x_0, x_1] - f[x_1, x_2])/(x_0 - x_2) f[x_0, x_1, ..., x_n] | = | (f[x_0, ..., x_(n - 1)] - f[x_1, ..., x_n])/(x_0 - x_n).

Horner's method | interpolation | Newton's divided difference interpolation formula | reciprocal difference