希尔伯特空间中线性逆问题的最优收敛速率结果
Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces.
作者信息
Albani V, Elbau P, de Hoop M V, Scherzer O
机构信息
Computational Science Center, University of Vienna , Vienna , Austria.
Department of Computational and Applied Mathematics and Department of Earth Science, Rice University , Houston , Texas , USA.
出版信息
Numer Funct Anal Optim. 2016 Feb 2;37(5):521-540. doi: 10.1080/01630563.2016.1144070. Epub 2016 Feb 8.
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.
在本文中，我们证明了用于求解希尔伯特空间中线性不适定算子方程的正则化方法的最优收敛速率结果。这些结果将现有的关于最优性的收敛速率结果推广到一般的源条件，如对数源条件。此外，我们还给出了变分源条件下的最优性结果，并展示了其与近似源条件的联系。
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