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 models, 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 $\mathcal{C}[-1,1]$.

最近，在最佳恢复的背景下研究了基于近似能力的模型。但是，这些模型与过度参数化不兼容，因为模型和数据一致的函数可能随后会受到限制。这个缺点促使引入具有附加有界条件的精炼近似模型。因此，本文提出了两种新模型：一种模型将有界性应用于目标函数（第一种类型），另一种模型将有界性应用于近似函数（第二种类型）。对于这两种类型的模型，在解决线性函数的有效构造之前，都首先在抽象级别上描述用于线性函数恢复的最佳映射。通过利用半定编程的技术，$\mathcal{C}[-\mathrm{1个}，\mathrm{1个}]$。