论文标题
在低阶源条件下对Tikhonov正则化的差异原理的分析
Analysis of the discrepancy principle for Tikhonov regularization under low order source conditions
论文作者
论文摘要
我们研究了Tikhonov正则化在不适合的非线性操作员方程中的应用。这项工作的目的是证明在对数类型的低阶源条件下，差异原理的低阶收敛速率。我们在希尔伯特量表的框架内工作，并将有关此主题的现有研究扩展到过度厚度的案例。后者意味着处理的操作员方程的精确解决方案不属于罚款定义的定义领域。结果，Tikhonov功能无法具有有限的值。
We study the application of Tikhonov regularization to ill-posed nonlinear operator equations. The objective of this work is to prove low order convergence rates for the discrepancy principle under low order source conditions of logarithmic type. We work within the framework of Hilbert scales and extend existing studies on this subject to the oversmoothing case. The latter means that the exact solution of the treated operator equation does not belong to the domain of definition of the penalty term. As a consequence, the Tikhonov functional fails to have a finite value.
