In this paper, we study optimization problems of numerical differentiation and summation methods on classes of univariate functions. Sharp estimates (in order) of the optimal recovery error and information complexity are calculated for these classes. Algorithms are constructed based on the truncation method and Chebyshev polynomials to implement these estimates. Moreover, we establish under what conditions the summation problem is well-posed.

翻译：本文研究了单变量函数类上数值微分与求和方法的优化问题。针对这些函数类，我们计算了最优恢复误差与信息复杂度的精确（阶）估计。基于截断方法与切比雪夫多项式构造了实现这些估计的算法。此外，我们建立了求和问题适定所需满足的条件。