Summary: ``How to choose regularization parameters is an important issue in Tikhonov regularization 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. Furthermore, two hybrid algorithms, the linear-to-linear model function algorithm and the hyperbolic-to-linear model function algorithm, are proposed with global convergence. Efficiency of the proposed algorithms is illustrated through numerical experiments.''