散乱数据的数值微分及其误差估计

1 背景及问题的提出 导数是数学分析中的一个基本的慨念。对于数学工作者来讲,计算导数不是一项特别困难的工作。但是,对于研究实际问题的科学工作者来讲,这项工作就不是一件简单的工作了,首先,求导数的问题是一个典型的Hadamard意义下的不适定问题(5],12]等)

THE NUMERICAL DIFFERENTIATION OF SCATTERED DATA AND IT'S ERROR ESTIMATE

Numerical differentiation of scattered data is a classified and important ill-posed problem. In this paper, we solve this problem by the Tikhonov regularization method. Based on the conditional stability estimate for this ill-posed problem, a new simple method for choosing regularization parameters is proposed. We show that our method has the similiar computational results but with much less computation, in comparison with other methods. The error estimate is also given. And the numerical results show that our method is simple and applicable.