High-order convergence methods for selecting the regularization parameter in linear inverse problem

Based on Tikhonov regularization method and the Morozov discrepancy principle, this paper presents three improved high-order convergence Newton iteration methods for choosing the regularization parameter in linear inverse problem. The detailed algorithm and the convergence rate estimation are given. Compared to the Newton method and the third-order convergence method, these three improved high-order convergence Newton iteration methods significantly reduce the number of iteration steps. Numerical simulation experiment of the inverse heat conduction problems(IHCP), which are very important problems in many engineering areas such as archaeology, reaction-diffusion process and the continuous casting of steel billets, illustrate the effectiveness of the proposed method.