算子及观测数据都非精确情况下一种新的正则参数选择方法

A NEW METHOD OF CHOOSING REGULARIZATION PARAMETER WITH PERTURBED OPERATOR AND NOISY DATA

在考虑算子及右端项都扰动的情况下,研究求解第一类算子方程的正则参数选择方法.提出了一种新的正则参数选择策略:即修正的广义偏差原则(MGDP)并进行了理论分析,数值试验则进一步证明了该方法的有效性.

Many inverse problems in mathematical physics can be considered as an operator equations of the first kind. Essentially, inverse problems are ill-posed, therefore regularization is a must. As is known, the choice of the regularization parameter is a key matter for ensuring proper regularization. The method of iterative choices of regularization parameter with perturbed operator and noisy data for solving operator equations of the first kind is investigated. A modified GDP for finding some reasonable regularization parameters in an efficient manner is proposed. Numerical experiments for integral equations of the first kind are presented to illustrate the efficiency of the proposed algorithms.