A note on numerical differentiation

Given the matrix $f = \{{f_i}\}$, representing $f\left ( x \right )$ at the set of points $\{ {x_i}\}$, the $m$th derivatives of $f\left ( x \right )$ at these points are expressed in terms of all of the ${f_i}$ according to ${f^{\left ( m \right )}} = {C^{ - 1}}{A^m}Cf$, where A is the sum of the skew matrix $\left [ {{{\left ( {{x_i} - {x_i}} \right )}^{ - 1}}} \right ]$ and the diagonal matrix formed by summing the terms in the corresponding rows of this skew matrix, and C is the diagonal matrix having as its elements the products of the elements in the corresponding rows of the skew matrix.