二维离散数据的数值微分问题的积分算子方法

2-D Numerical Differentiation by Integral Operator

二维离散数据的数值微分问题是典型的不适定问题。基于GROETSCH的思想,提出了利用积分算子方法来构造近似偏导数和方向导数的方法,并将该方法用于二维离散数据的数值微分问题,并给出了误差估计。数值实验表明该方法是有效的。

The numerical differentiation question of two-dimensional discrete data is a typical ill-posed problem.Based on the thought of Groetsch,an integral operator method to construct the approximate partial derivative and directional derivative was proposed.The method was then used in the numerical differentiation question of two-dimensional discrete data,and the error estimate was given.