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

The Arnoldi-Fractional Tikhonov algorithms for Solving Large Scale Linear Discrete Ill-posed Problems

随着科技发展,不适定问题出现在地球物理等多种领域。正则化方法是求解此类问题近似解的有效算法。该文将Fractional Tikhonov正则化算法应用于投影算法,提出求解大规模线性离散不适定问题的Arnoldi-Fractional Tikhonov正则化算法。并进一步提出广义Arnoldi-Fractional Tikhonov正则化算法。最后,论文对所提出的算法编写程序进行数值试验比较。结果表明新算法是有效且具有优势的。

With the development of the technology,the ill-posed problems widely arise in many areas such as geophysics and so on. In this thesis, An Arnoldi-Fractional Tikhonov regularization method for large scale linear discrete ill-posed problems is presented via applying the Fractional Tikhonov regularization to the projection algorithm. Further more, the generalized ArnoldiFractional Tikhonov method are proposed in the follows. At last, this thesis conducts numerous classical numerical experiments on the improved methods proposed above. Numerical experiments and comparisons indicate that the new improved regularization methods are feasible and efficient.