算子非精确条件下确定正则化参数的一种方法

基于非标准的广义偏差原则,在算子及观测数据都有扰动的条件下,对于求解不适定问题的Tik-honov正则化方法,给出了一种选取正则化参数的简单迭代算法,并阐明了该迭代算法是一种线性模型函数算法.进一步地,利用线性模型函数方法,在一定条件下证明了所提出的选取正则化参数的简单迭代算法是收敛的,并通过数值算例验证了该方法的有效性.

The Method for Determining Regularization Parameters with Perturbed Operators

Based on the non-standard generalized discrepancy principle,a simple iteration method is given for choosing regularization parameters with perturbed operator and noise data for the Tikhonov regularization method,which is a classical method for solving ill-posed problems.And it is clarified that the proposed iteration method is a linear model function algorithm.Furthermore,the simple iteration method for choosing regularization parameters is proved to be converging under some conditions by using the linear model function method.Numerical experiments show that the method is efficient.