The article is devoted to a generalized setting of adaptive recovery from noisy information. We extend some known results for this setting and obtain sufficient conditions under which adaption does not help for recovery of linear operators. For recovery of linear functionals we give necessary and sufficient conditions for the existence of an optimal nonadaptive linear method which gives the same error as optimal adaptive methods.

中文翻译：

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从嘈杂信息中进行广义自适应与非自适应恢复

本文致力于从嘈杂信息中自适应恢复的一般设置。我们扩展了此设置的一些已知结果，并获得了充分的条件，在这些条件下自适应对恢复线性算子没有帮助。为了恢复线性泛函，我们给出了存在最优非自适应线性方法的必要和充分条件，该非自适应线性方法的误差与最优自适应方法相同。