On convergence rates for iteratively regularized procedures with linear penalty terms
On convergence rates for iteratively regularized procedures with linear penalty terms
复制标题
关于具有线性罚项的迭代正则化过程的收敛率
DOI：
10.1088/0266-5611/28/8/085005
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发表时间：
2012
期刊：
影响因子：
2.1
通讯作者：
A. Smirnova
中科院分区：
文献类型：
--
作者：
A. Smirnova
本文件的影响是双重的。首先，我们研究了迭代正则化高斯-牛顿（IRGN）算法的收敛速度与线性惩罚项下广义源的假设，并显示新的迭代的正则化性能取决于解决方案的光滑性。其次，我们介绍了一个自适应IRGN过程，这是在放松光滑条件下进行研究。引入和分析一个更一般的惩罚项是非常重要的，因为除了带来稳定的数值方案，旨在解决一大类应用反问题，它使我们能够将各种类型的先验信息模型。先验和后验停止规则进行了研究。对于先验停止规则，最优收敛速度。一个数值例子说明收敛速度。
The impact of this paper is twofold. First, we study convergence rates of the iteratively regularized Gauss–Newton (IRGN) algorithm with a linear penalty term under a generalized source assumption and show how the regularizing properties of new iterations depend on the solution smoothness. Secondly, we introduce an adaptive IRGN procedure, which is investigated under a relaxed smoothness condition. The introduction and analysis of a more general penalty term are of great importance since, apart from bringing stability to the numerical scheme designed for solving a large class of applied inverse problems, it allows us to incorporate various types of a priori information available on the model. Both a priori and a posteriori stopping rules are investigated. For the a priori stopping rule, optimal convergence rates are derived. A numerical example illustrating convergence rates is considered.
影响因子：
2.9
作者：
Bauer, Frank;Hohage, Thorsten;Munk, Axel
通讯作者：
Munk, Axel