Discrepancy principles for Tikhonov regularization of ill-posed problems leading to optimal convergence rates

1987 ◽  
Vol 52 (2) ◽  
pp. 209-215 ◽  
Author(s):  
H. W. Engl
Keyword(s):  
Tikhonov Regularization ◽  
Convergence Rates ◽  
Optimal Convergence ◽  
Optimal Convergence Rates ◽  
Ill Posed

scholarly journals Optimal Convergence Rates for Tikhonov Regularization in Besov Spaces

2020 ◽  
Vol 58 (1) ◽  
pp. 21-47 ◽  
Author(s):  
Frederic Weidling ◽  
Benjamin Sprung ◽  
Thorsten Hohage
Keyword(s):  
Tikhonov Regularization ◽  
Besov Spaces ◽  
Convergence Rates ◽  
Optimal Convergence ◽  
Optimal Convergence Rates

scholarly journals Multiscale Compression Algorithm for Solving Nonlinear Ill-Posed Integral Equations via Landweber Iteration

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 221
Author(s):  
Rong Zhang ◽  
Fanchun Li ◽  
Xingjun Luo
Keyword(s):  
Theoretical Analysis ◽  
Galerkin Method ◽  
Integral Equations ◽  
Convergence Rates ◽  
Numerical Results ◽  
Compression Algorithm ◽  
Optimal Convergence ◽  
Relaxation Factor ◽  
Optimal Convergence Rates ◽  
Ill Posed

In this paper, Landweber iteration with a relaxation factor is proposed to solve nonlinear ill-posed integral equations. A compression multiscale Galerkin method that retains the properties of the Landweber iteration is used to discretize the Landweber iteration. This method leads to the optimal convergence rates under certain conditions. As a consequence, we propose a multiscale compression algorithm to solve nonlinear ill-posed integral equations. Finally, the theoretical analysis is verified by numerical results.

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