In this article we investigate the connection between regularization theory for inverse problems and dynamic programming theory. This is done by developing two new regularization methods, based on dynamic programming techniques. The aim of these methods is to obtain stable approximations to the solution of linear inverse ill-posed problems. We follow two different approaches and derive a continuous and a discrete regularization method. Regularization properties for both methods are proved as well as rates of convergence. A numerical benchmark problem concerning integral operators with convolution kernels is used to illustrate the theoretical results.

翻译：在本条中,我们调查反向问题的正规化理论与动态编程理论之间的联系,这是通过在动态编程技术的基础上开发两种新的正规化方法实现的。这些方法的目的是为解决线性反向问题取得稳定的近似值。我们遵循两种不同的方法,并得出一种连续和独立的正规化方法。两种方法的正规化特性以及趋同率都得到了证明。使用关于集成内核整体操作者的数字基准问题来说明理论结果。