Expanding the applicability of an a posteriori parameter choice strategy for Tikhonov regularization of nonlinear ill-posed problems

2019 ◽  
Vol 113 (3) ◽  
pp. 2813-2826
Author(s):  
Ioannis K. Argyros ◽  
Yeol Je Cho ◽  
Santhosh George ◽  
Yi-bin Xiao
Keyword(s):  
Tikhonov Regularization ◽  
A Posteriori ◽  
Parameter Choice ◽  
Choice Strategy ◽  
A Posteriori Parameter Choice ◽  
Ill Posed ◽  
Parameter Choice Strategy

On the Parameter Choice in the Multilevel Augmentation Method

2020 ◽  
Vol 20 (3) ◽  
pp. 555-571
Author(s):  
Suhua Yang ◽  
Xingjun Luo ◽  
Chunmei Zeng ◽  
Zhihai Xu ◽  
Wenyu Hu
Keyword(s):  
Tikhonov Regularization ◽  
Regularization Method ◽  
Numerical Experiments ◽  
Convergence Rates ◽  
Tikhonov Regularization Method ◽  
Fredholm Integral Equations ◽  
Parameter Choice ◽  
Choice Strategy ◽  
Ill Posed ◽  
Parameter Choice Strategy

AbstractIn this paper, we apply the multilevel augmentation method for solving ill-posed Fredholm integral equations of the first kind via iterated Tikhonov regularization method. The method leads to fast solutions of the discrete regularization methods for the equations. The convergence rates of iterated Tikhonov regularization are achieved by using a modified parameter choice strategy. Finally, numerical experiments are given to illustrate the efficiency of the method.

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