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首页> 外文期刊>Journal of complexity >Instances of computational optimal recovery: Refined approximability models
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Instances of computational optimal recovery: Refined approximability models

机译：计算最佳恢复的实例：精制近似性模型

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摘要

Models based on approximation capabilities have recently been studied in the context of Optimal Recovery. These models, however, are not compatible with overparametrization, since modeland 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 C[-1, 1]. (c) 2020 Elsevier Inc. All rights reserved.
机译：最近在最佳恢复的背景下研究了基于近似能力的模型。然而，这些模型与过度分度化不兼容，因为型号和数据 - 一致的函数可以无限制。该缺点激励引入具有额外的界限条件的精制近似性模型。因此，在本文中提出了两个新模型：界限适用于目标函数（第一类型）和界限适用于近似值（第二类型）的那个新模型。对于两种类型的模型，首先在解决其有效结构之前的抽象水平上描述了用于恢复线性功能的最佳映射。通过从SEMIDEFINITE编程中利用技术，这些结构明确地在涉及C [-1,1]的多项式子空间的常见例子上进行。 （c）2020 Elsevier Inc.保留所有权利。

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