The problem of recovering partial derivatives of high orders of bivariate functions with finite smoothness is studied. Based on the truncation method, a numerical differentiation algorithm was constructed, which is optimal by the order, both in the sense of accuracy and in the sense of the amount of Galerkin information involved. Numerical demonstrations are provided to illustrate that the proposed method can be implemented successfully.

翻译：研究了光滑性有限的二元函数高阶偏导数的恢复问题。基于截断方法，构造了一种数值微分算法，该算法在精度和涉及的Galerkin信息量意义上均达到了阶最优。提供了数值演示，以说明所提出的方法能够成功实施。