Title of article :
MODIFICATION OF THE TIKHONOV METHOD UNDER SEPARATE RECONSTRUCTION OF COMPONENTS OF SOLUTION WITH VARIOUS PROPERTIES
Author/Authors :
Vasin, V.V. N. N. Krasovskii Institute of Mathematics and Mechanics UB RAS - Ural Federal University, Ekaterinburg, Russia , Belyaev, V.V. N. N. Krasovskii Institute of Mathematics and Mechanics UB RAS - Ural Federal University, Ekaterinburg, Russia
Abstract :
In this paper a linear ill-posed is considered. Its solution is given in the form of a
sum of two components: one contains breaks and the other is continuous, but admits breaks
of derivative. For stable separate reconstruction of a solution, a modified Tikhonov method is
applied. In this method, the stabilizer is chosen as a sum of two functionals with using total
variation of function and its derivative, where every stabilizing functional depends on one
component only. The convergence of the sum of the regularized components to a solution of
the initial problem is proved. A scheme of finite-dimensional approximations of the regularized
problem is investigated and the results of numerical experiments are presented.
Keywords :
ill-posed problem , Tikhonov regularization , non-smooth solution , total variation
Journal title :
Eurasian Journal of Mathematical and Computer Applications
