论文标题
通过mollification对线性和非线性不良问题的正则化
Regularization of linear and nonlinear ill-posed problems by mollification
论文作者
论文摘要
在本文中，我们解决了使用Mollification近似解决问题的解决方案的问题。我们迅速审查现有的摩尔化正则化方法，并为通用不良方程式$ t（f）= g $提供两个新的近似解决方案，其中$ t $可能是非线性的。我们定义的正则解决方案扩展了Bonnefond和Maréchal\ cite {XAPI}的工作，并追踪它们的起源在我们所知的各种变化表述中，首先是Lannes等人引入的。 \ cite {lannes}。除了一致性结果之外，我们还是第一次，我们为通过变异公式定义的微弱方法提供了一些收敛速率。
In this paper, we address the problem of approximating solutions of ill-posed problems using mollification. We quickly review existing mollification regularization methods and provide two new approximate solutions to a general ill-posed equation $T(f) =g$ where $T$ can be nonlinear. The regularized solutions we define extend the work of Bonnefond and Maréchal \cite{xapi}, and trace their origins in the variational formulation of mollification, which to the best of our knowledge, was first introduced by Lannes et al. \cite{lannes}. In addition to consistency results, for the first time, we provide some convergence rates for a mollification method defined through a variational formulation.
