Functional error estimators for the adaptive discretization of inverse problems
Functional error estimators for the adaptive discretization of inverse problems
复制标题
用于逆问题自适应离散化的函数误差估计器
DOI：
10.1088/0266-5611/32/10/104004
复制
发表时间：
2015
期刊：
影响因子：
2.1
通讯作者：
D. Wachsmuth
中科院分区：
文献类型：
--
作者：
Christian Clason;B. Kaltenbacher;D. Wachsmuth
所谓的函数误差估计器为可靠地估计两个凸函数之和的离散化误差提供了一个有价值的工具。我们将这一概念应用到Tikhonov正则化的偏微分方程反问题的解决方案，不仅为二次希尔伯特空间正则化条款，但也为非光滑Banach空间的罚款。示例包括测量空间范数（即，稀疏正则化）或L ∞球的指示函数（即，Ivanov正则化）。误差估计量可以用最优性系统中的残差来表示，然后可以用传统的方法来估计，从而得到显式的估计量。这是说明了一个椭圆形的反源问题与上述罚款，并提供了稀疏正则化的情况下的数值结果。
So-called functional error estimators provide a valuable tool for reliably estimating the discretization error for a sum of two convex functions. We apply this concept to Tikhonov regularization for the solution of inverse problems for partial differential equations, not only for quadratic Hilbert space regularization terms but also for nonsmooth Banach space penalties. Examples include the measure-space norm (i.e., sparsity regularization) or the indicator function of an L ∞ ball (i.e., Ivanov regularization). The error estimators can be written in terms of residuals in the optimality system that can then be estimated by conventional techniques, thus leading to explicit estimators. This is illustrated by means of an elliptic inverse source problem with the above-mentioned penalties, and numerical results are provided for the case of sparsity regularization.
影响因子：
2.1
作者：
Kaltenbacher, B.;Kirchner, A.;Veljovic, S.
通讯作者：
Veljovic, S.
影响因子：
2.1
作者：
Kaltenbacher, B.;Kirchner, A.;Vexler, B.
通讯作者：
Vexler, B.