THE MODIFIED TIKHONOV REGULARIZATION METHOD WITH THE SMOOTHED TOTAL VARIATION FOR SOLVING THE LINEAR ILL-POSED PROBLEMS
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Published:2021-06
Issue:2
Volume:9
Page:88-100
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ISSN:2306-6172
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Container-title:Eurasian Journal of Mathematical and Computer Applications
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language:
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Short-container-title:EJMCA
Author:
Vasin Vladimir, ,Belyaev Vladimir
Abstract
We investigate a linear operator equation of the first kind that is ill-posed in the Hadamard sence. It is assumed that its solution is representable as a sum of smooth and discontinuous components. To construct a stable approximate solutions, we use the modified Tikhonov method with the stabilizing functional as a sum of the Lebesgue norm for the smooth component and a smoothed BV-norm for the discontinuous component. Theorems of exis- tence, uniqueness, and convergence both the regularized solutions and its finite-dimentional approximations are proved. Also, results of numerical experiments are presented.
Publisher
L. N. Gumilyov Eurasian National University
Subject
Applied Mathematics,Computational Mathematics,Computer Science Applications,Mathematical Physics,Modelling and Simulation,Information Systems