中文摘要：

1引言 根据带误差的测量数据重构函数使其微分能较好的拟合精确函数微分，是一个有重要意义的研究课题，在图像处理、计算机视觉和计算力学等领域中均有应用[2,3，4]．

英文摘要：

In this paper a new numerical differentiation algorithm with regularization, based on the prescribed data with measurement error is proposed. It retains the similar global error estimate as for the existing algorithm, but avoids some drawback of the latter one （bad approximation near the end points of the region of interest）. The new algorithm has a unique solution and the corresponding characterization conditions are established. In addition, the error estimate is developed in the square integrable norm. Finally, numerical tests are provided to show the effectiveness of our algorithm. In particular, in the case of small size of samples, our algorithm performs better than the original algorithm.