  An explicit formula to approximate the diagonal entries of the Hessian is
introduced. When the derivative-free technique called \emph{generalized
centered simplex gradient} is used to approximate the gradient, then the
formula can be computed for only one additional function evaluation. An error
bound is introduced and provides information on the form of the sample set of
points that should be used to approximate the diagonal of a Hessian. If the
sample set of points is built in a specific manner, it is shown that the
technique is $\mathcal{O}(\Delta_S^2)$ accurate approximation of the diagonal
entries of the Hessian where $\Delta_S$ is the radius of the sample set.
