基于埃特金加速的改进Landweber迭代正则化方法

Modified Landweber Iteration Regularization Method Based on Aitken Acceleration

为克服Landweber迭代正则化方法在求解大规模不适定问题时收敛速度慢的不足,将埃特金加速技巧与不动点迭代相结合,构建了能快速收敛的改进Landweber迭代正则化方法.数值实验结果表明:改进的迭代正则化方法在稳定求解不适定问题时,能够快速地收敛至问题的最优解,较Landweber迭代正则化方法大大提高了收敛速度.

To overcome the disadvantage of slow convergence of the standard Landweber iteration regularization method in solving large-scale ill-posed problems,in this paper,we propose a modified Landweber iteration regularization method by combining the Aitken acceleration skill and fixed-point iteration.Numerical experiments show that the modified iteration regularization method can converge to the optimal robust solution and improve the convergence rate greatly,compared with the standard Landweber iteration regularization method.