论文标题
计算最佳恢复的实例：精致的近似值模型
Instances of Computational Optimal Recovery: Refined Approximability Models
论文作者
论文摘要
最近在最佳恢复的背景下研究了基于近似功能的模型。但是，这些模型与过度隔离不合适，因为模型和数据一致的函数可能会不受限制。这种缺点促使引入具有附加性条件的精致近似值模型。因此，在本文中提出了两个新模型：一个界限适用于目标函数（第一种类型）的其中，一个界限适用于近似值（第二类）。对于两种类型的模型，在解决其有效构造之前，首先在抽象级别上以抽象级别描述用于恢复线性功能的最佳图。通过从半决赛编程中利用技术，这些结构是在一个涉及$ \ MATHCAL {C} [C} [-1,1] $的多项式子空间的常见示例上明确执行的。
Models based on approximation capabilities have recently been studied in the context of Optimal Recovery. These models, however, are not compatible with overparametrization, since model- and data-consistent functions could then be unbounded. This drawback motivates the introduction of refined approximability models featuring an added boundedness condition. Thus, two new models are proposed in this article: one where the boundedness applies to the target functions (first type) and one where the boundedness applies to the approximants (second type). For both types of model, optimal maps for the recovery of linear functionals are first described on an abstract level before their efficient constructions are addressed. By exploiting techniques from semidefinite programming, these constructions are explicitly carried out on a common example involving polynomial subspaces of $\mathcal{C}[-1,1]$.
