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.

翻译：引入了接近赫森语对角条目的明确公式。 当使用名为 emph{ 通用中心偏向坡度} 的无衍生物技术来接近梯度时, 公式只能为另外一项函数评价计算。 引入了错误, 并提供了关于一组样本点的形式的信息, 这些样本点应该用来接近赫森语的对角。 如果以特定方式构建了一组样本点, 则显示该技术是 $\ mathcal{ O} (\\ Delta_ S% 2) 的赫森语对角点的准确近似值, 其中 $\ Delta_ S$ 是样本集的半径 。