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ON REGULAR RECOVERY ALGORITHM FOR NON-SMOOTH SOLUTIONS OF FREDHOLM INTEGRAL EQUATIONS OF THE FIRST KIND

Т. I. Serezhnikova
VANT. Ser.: Mat. Mod. Fiz. Proc 2010. Вып.4. С. 71-78.

Analyzed here is the technique and numerical experiments for (one-dimensional) Fredholm integral equations of the first kind at geophysical field extension and antenna synthesis.
The regular algorithm is based on Tykhonov regularity using Lipschitz space norm function as a stabilizer, additional use of prox-technique and subgradient processes for non-smooth minimization problems. The short description of the used convergence theorems (with references) and subgradients applicability is given.
Simulation results are described; estimated accuracy is given as well as recommendations for practical parameterization of computations and accuracy control.
Numerical experiments confirm that the suggested technique can be used in mathematical simulation of various applied problems to reestablish Fredholm integral equation of the first kind. The given technique can be used to reestablish smooth (continuous) solutions, as well as kinked, discontinuous, maximum-close solutions.

Keywords: Fredholm integral equation, non-smooth solution, Tykhonov regularity, proximal method, subgradient process.








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