Abstract

A modification for the definition of an a posteriori error estimate for a regularizing algorithm for solving an ill-posed problem is proposed. We introduce, analyze and illustrate by examples the concept of a uniformly a posteriori error estimate for a regularizing algorithm. A necessary and sufficient condition for the existence of a regularizing algorithm satisfying such an estimate is established. The class of conditionally well-posed problems is characterized in terms of regularizability with uniformly a posteriori error estimates.

中文翻译：

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均匀化后验误差估计以进行正则化算法

摘要

提出了一种修改后验误差估计的定义，用于解决不适定问题的正则化算法。我们通过示例介绍，分析和说明用于正则化算法的统一后验误差估计的概念。建立了满足这种估计的正则化算法的存在的充要条件。一类条件良好的问题的特征在于具有后验误差估计的可正则性。