Abstract

The construction of optimal interpolation formulas is discussed. First, an exact upper bound for the error of an interpolation formula in the Sobolev space is calculated. The existence and uniqueness are proved for the optimal interpolation formula with the smallest error. An algorithm for finding the coefficients of the optimal interpolation formula is presented. This algorithm makes it possible to find the optimal coefficients.

中文翻译：

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论函数的最优插值

摘要

讨论了最优插值公式的构造。首先，计算 Sobolev 空间中插值公式的误差的精确上限。证明了误差最小的最优插值公式的存在性和唯一性。提出了一种寻找最佳插值公式系数的算法。该算法可以找到最佳系数。