标题： 噪声数据的最优线性逼近器 显示英文标题

标题： Optimal linear approximants for noisy data

摘要： 本文介绍了针对处理点值噪声数据的线性逼近方法。 一个关键创新在于通过求解旨在最小化噪声方差的优化问题来确定逼近系数。 本研究解决了普遍情况，允许数据之间存在噪声相关性，并且数据分布不均匀。 事实上，我们证明了[S. López-Ureña和D. F. Yáñez, J. Sci. Comput., 100(1) (2024)]中提出的细分规则对于非均匀方差的不相关噪声是最佳的。 提供了数值实验以展示这些最优逼近方法与其他方法相比的有效性。 显示英文摘要

摘要： This paper introduces linear approximants tailored to handle point-valued noisy data. A key innovation lies in determining the approximant coefficients by solving an optimization problem aimed at minimizing the noise variance. The study addresses the general case, allowing for noise correlation among data with a non-uniform distribution. In fact, we show that the subdivision rules proposed in [S. L\'opez-Ure\~na and D. F. Y\'a\~nez, J. Sci. Comput., 100(1) (2024)] are optimal for uncorrelated noise with non-uniform variance. Numerical experiments are provided to demonstrate the effectiveness of these optimal approximants compared to other ones.