Given pointwise samples of an unknown function belonging to a certain model set, one seeks in Optimal Recovery to recover this function in a way that minimizes the worst-case error of the recovery procedure. While it is often known that such an optimal recovery procedure can be chosen to be linear, e.g. when the model set is based on approximability by a subspace of continuous functions, a construction of the procedure is rarely available. This note uncovers a practical algorithm to construct a linear optimal recovery map when the approximation space is a Chevyshev space of dimension at least three and containing the constant functions.
翻译：考虑到属于某种模型集的未知功能的点点样,人们在最佳回收中寻求以尽量减少回收程序最坏的错误的方式恢复这一功能,虽然人们通常知道,这种最佳回收程序可以选择为线性,例如,当模型集基于连续功能子空间的接近性,对程序的构建极少。本说明揭示了当近似空间至少为三维维谢夫空间并包含常数功能时,构建线性最佳回收图的实用算法。
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