An a Posteriori Parameter Choice for Tikhonov Regularization in Hilbert Scales Leading to Optimal Convergence Rates

1988 ◽  
Vol 25 (6) ◽  
pp. 1313-1326 ◽  
Author(s):  
Andreas Neubauer
Keyword(s):  
Tikhonov Regularization ◽  
Convergence Rates ◽  
A Posteriori ◽  
Parameter Choice ◽  
Optimal Convergence ◽  
Optimal Convergence Rates ◽  
A Posteriori Parameter Choice

Multiscale Galerkin methods for the nonstationary iterated Tikhonov method with a modified posteriori parameter selection

2018 ◽  
Vol 26 (1) ◽  
pp. 109-120
Author(s):  
Xingjun Luo ◽  
Zhaofu Ouyang ◽  
Chunmei Zeng ◽  
Fanchun Li
Keyword(s):  
Convergence Rates ◽  
Regularization Parameter ◽  
Fredholm Integral Equations ◽  
Galerkin Methods ◽  
A Posteriori ◽  
Parameter Choice ◽  
Compression Technique ◽  
Choice Strategy ◽  
Optimal Convergence Rates ◽  
Parameter Choice Strategy

AbstractIn this paper, we consider a fast multiscale Galerkin method with compression technique for solving Fredholm integral equations of the first kind via the nonstationary iterated Tikhonov regularization. A modified a posteriori regularization parameter choice strategy is established, which leads to optimal convergence rates.

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