求解大规模线性离散不适定问题的RRArnoldi-Fractional Tikhonov正则化算法

An Arnoldi-Fractional Tikhonov Regularization Algorithm for Solving Large Scale Linear Discrete Ill Posed Problems

不适定问题广泛出现在地球物理、自动控制等多种领域.正则化方法是求解此类问题近似解的有效算法.将Fractional Tikhonov正则化算法应用于投影算法,提出了求解大规模线性离散不适定问题的Arnoldi-Fractional Tikhonov正则化算法.进一步提出限制值域的Arnoldi-Fractional Tikhonov正则化算法.并针对经典算例,进行了数值试验和比较.数值试验结果表明了新算法是有效且具有优势的.

The ill posed problems are widely presented in many fields such as geophysics, automatic control and so on. The regularization method is an effective method to solve the approxi- mate solution of this kind of problem. In this paper, the Fractional Tikhonov regularization algorithm is applied to the projection algorithm. Firstly, an Arnoldi-Fractional Tikhonov regularization algorithm is proposed for solving large-scale linear discrete ill posed problems. Secondly, an Arnoldi-Fractional Tikhonov regularization algorithm of restricted range is put forward. And numerical experiments and comparisons are carried out for the classical examples. The numerical experiment results show that the new algorithm is effective and has more advantages.