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Abstract <p>For the ill-posed problem of approximating the value of a discontinuous mapping, a theorem is proved that provides a necessary and sufficient condition for the regularizability of this problem with an a posteriori accuracy estimate for the resulting approximation. The result is illustrated by examples of inverse problems with various sets of a priori constraints.</p>

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Which Ill-Posed Problems Are Regularizable with A Posteriori Accuracy Estimates?

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • M. Yu. Kokurin

摘要

Abstract

For the ill-posed problem of approximating the value of a discontinuous mapping, a theorem is proved that provides a necessary and sufficient condition for the regularizability of this problem with an a posteriori accuracy estimate for the resulting approximation. The result is illustrated by examples of inverse problems with various sets of a priori constraints.