The problems of optimal recovery of unbounded operators are studied. Optimality means the highest possible accuracy and the minimal amount of discrete information involved. It is established that the truncation method, when certain conditions are met, realizes the optimal values of the studied quantities. As an illustration of the general results, problems of numerical differentiation and the backward parabolic equation are considered.

翻译：本文研究了无界算子的最佳恢复问题。最佳性体现在追求最高可能的精度与最少离散信息量的结合。研究证明，在满足特定条件时，截断方法能够实现所研究量的最优值。作为一般性结论的例证，本文具体探讨了数值微分问题及反向抛物型方程的求解。