中文摘要：

如何选取正则化参数是不适定问题Tikhonov正则化的一个重要问题．基于吸收的Morozov偏差原理，研究了正则化参数选取的线性模型函数方法．在从Hermite插值角度导出线性模型函数后，讨论了选取正则化参数的两种线性模型函数算法（基本算法与改进算法）及其收敛性．为克服基本算法的局部收敛性，提出了一种新的线性模型函数松弛算法．并且，提出了两种具有全局收敛性的组合算法，即线性与线性模型函数算法、双曲型与线性模型函数算法．数值实验说明了所提算法的有效性．

英文摘要：

How to choose regularization parameters is an important issue in Tikhonov regular- ization of ill-posed problems. Based on the damped Morozov discrepancy principle, this paper studies the linear model function method for choosing regularization parameters. The linear model function is derived from the point of view of the Hermite interpolation, and two linear model function algorithms （a basic algorithm and a modified algorithm） with their convergence results are discussed for choosing regularization parameters. Then, a new relaxation algorithm for the linear model function is proposed to overcome the local convergence of the basic algorithm. Fur- thermore, two hybrid algorithms, the linear-to-linear model function algorithm and the hyperbolic-to-linear model function algorithm, are proposed with global con- vergence. Efficiency of the proposed algorithms is illustrated through numerical experiments.