未知目标函数之一阶数值微分公式验证与实践

根据多项式插值理论，对于未知的目标函数，在离散采样点获取其对应的函数值后，即可构造Lagrange插值多项式以近似求得该未知函数的逼近表达式．进而，对Lagrange插值多项式求一阶导数可得到该未知目标函数的多点一阶微分近似公式；即：等间距情况下的2～16个数据点的后向差分公式．计算机数值实验进一步验证与表明：该用于未知目标函数一阶数值微分的多点公式可以取得较高的计算精度．

Verification and Practice on First-Order Numerical Differentiation Formulas for Unknown Target Functions

Based on the polynomial-interpolation theory, the Lagrange interpolating polynomial could be constructed by using the corresponding discrete-time values of an unknown target-function. Then,the approximate first-order numerical-differentiation formulas could be derived in terms of those multiple sampiing-nodes. Hence, the equally-spaced backward-difference formulas involving two to sixteen samplingnodes. Experimental results verify that the relatively high computational-precision could be achieved by using these formulas, when estimating the numerical values of the first-order derivative of unknown targetfunctions are estimated.