基于Landweber-Kaczmarz正则化方法的参数重构

Reconstructing parameter by using Landweber-Kaczmarz regularization method

正则化方法在经济学和工程学参数重构中起到极为重要作用.传统Landweber正则化方法主要是在观测数据带有噪音条件下重构参数,噪音水平往往是固定的单一数值.对于观测数据噪音水平不一致情况下,设计Landweber-Kaczmarz正则化方法重构参数.数值算例表明,Landweber-Kaczmarz正则化方法是收敛和稳定的,与传统Landweber正则化方法相比具有较高精度.

Regularization method for reconstructing parameter plays an important role in economics and engineering. The traditional Landweber regularization method is mainly to reconstruct the parameters with noisy observation data,and the noise level is often a single fixed value. In this paper,the Landweber-Kaczmarz regularization algorithm was designed to reconstruct the parameters when the noise level of the observation data was varied. Numerical examples showed that the Landweber-Kaczmarz regularization method was convergent and stable,and has higher accuracy compared with the traditional Landweber regularization method.