The problems of optimal recovering univariate functions and their derivatives are studied. To solve these problems, two variants of the truncation method are constructed, which are order-optimal both in the sense of accuracy and in terms of the amount of involved Galerkin information. For numerical summation, it has been established how the parameters characterizing the problem being solved affect its stability.

翻译：本文研究了单变量函数及其导数的最优恢复问题。为解决这些问题，构造了两种截断方法的变体，它们在精度意义和所用伽辽金信息量方面均具有阶次最优性。对于数值求和问题，已明确表征所求解问题的参数如何影响其稳定性。