术语“一阶导数”的详细信息

英译术语:

first derivative

汉语语境:

根据数值微分理论，若给定未知目标函数在指定区间上的离散采样点数据，可使用数值差分公式求目标点处的一阶导数近似值。但对于靠近边界的目标点而言，多点中心差分公式可能因单边数据点不足而无法使用。另外，目标函数的一阶导数在目标点处可能发生加速变化，而前(后)向差分公式只考虑了单边数据点，可能无法适应该变化，使导数值误差较大。

英语语境:

Based on the numerical differential theory, it is available to calculate the approximate first derivative of the target-node by using numerical differentiation formula when the discrete sampling points of the unknown target function on specified interval are given. But for the target-nodes close to the boundary, it may be unable to use the center differentiation formula involving multiple nodes because of the lack of sampling points on one side of the target-node. Besides, an accelerating change of the first derivative of the target-node may occur in some target functions. However, the use of forward(backward) differentiation formula simply takes the nodes on one side of the target-node into consideration, which probably makes the formula difficult to adapt to such a change, and thus leads to less accuracy in estimating the first derivative of the target-node.