关于不适定问题的迭代Tikhonov正则化方法  

On the iterated Tikhonov regularization for ill-posed problems

作　　者：张路寅[1] 张玉海[1] 钱坤明[1] 

机构地区：[1]山东大学数学学院,山东济南250100

出　　处：《山东大学学报（理学版）》2011年第4期29-33,共5页Journal of Shandong University(Natural Science)

摘　　要：讨论了求解不适定问题Kx=y的迭代Tikhonov正则化方法:xα0=0,(αI+K*K)xmα=K*y+αxm-1α,m=1,2,…。文中将参数α取为固定常数(α>0),这时迭代次数m起到正则化参数的作用。推导出正则滤波函数的性质,给出正则化参数m的先验估计m=m(α,δ)=O(αδ-2/(2r+1)),r≥0,证明了误差估计的收敛阶达到最优。在实际中,这种方法比将α看作正则化参数更容易计算。数值例子验证了理论结果。The iterated Tikhonov regularization for solving ill-posed problems is considered： x0α=0,（αI＋K＊K）xmα=K＊y＋αxm-1α,m=1,2,… The parameter m plays the role of the regularization parameter when the parameter α0 is fixed in this method.we deduce the property of regularizing filter function,give a priori optimal choice of m（α,δ）=O（αδ-2 2r＋1）,r≥0 and obtain optimal order of convergence.In practice,it is more convenient than viewing α as the regularization parameter for computation.Finally,a numerical example is included to verify the theoretical results.

关 键 词：不适定问题 迭代Tikhonov正则化 先验估计 收敛阶 

分 类 号：O241[理学—计算数学]