ABSTRACT In this article, we prove optimal convergence rates results for regularization methods for solving linear ill-posed operator equations in Hilbert spaces. The results generalizes existing convergence rates results on optimality to general source conditions, such as logarithmic source conditions. Moreover, we also provide optimality results under variational source conditions and show the connection to approximative source conditions.

中文翻译：

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希尔伯特空间中线性反问题的最优收敛率结果


摘要 在本文中，我们证明了求解希尔伯特空间中的线性不适定算子方程的正则化方法的最佳收敛率结果。结果将现有的收敛率结果推广到一般源条件（例如对数源条件）的最优性。此外，我们还提供了变分源条件下的最优性结果，并显示了与近似源条件的联系。