中文摘要：

本文研究了一阶数值微分问题,将其等价转化为第一类积分方程的求解问题,给出了求解该问题的局部正则化方法.在精确导数的一定假设条件下,讨论了正则化参数的先验选取策略及相应近似导数的误差估计.相对于经典的正则化方法,数值实验表明局部正则化方法能在有效抑制噪声的同时,保证近似导数逼近精确导数的效果,尤其是在精确导数有间断或急剧变化时.

英文摘要：

The first-order numerical differentiation problem is considered in this paper.By expressing the numerical differentiation problem as an integral equation of the first kind,the local regularization method is constructed for solving this problem approximately.Numerical experiments show that the local regularization method can ensure the accuracy of the approximate derivatives while suppressing the noise effectively,especially when the exact derivatives are discontinuous or changed sharply.