Pereverzev S. V.

Articles: 14

Article (Russian)

Optimal discretization of Ill-posed problems

Pereverzev S. V., Solodkii S. G.

↓ Abstract | Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 1. - pp. 106-121

We present a survey of results on the optimal discretization of ill-posed problems obtained in the Institute of Mathematics of the Ukrainian National Academy of Sciences.

Article (Russian)

Optimal methods for specifying information in the solution of integral equations with analytic kernels

Azizov M., Pereverzev S. V.

↓ Abstract | Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 5. - pp. 656-664

We determine the exact order of the minimum radius of information in the logarithmic scale for Fredholm integral equations of the second kind with periodic analytic kernels and free terms. We show that the information complexity of the solution of Fredholm equations with analytic kernels is greater in order than the complexity of the approximation of analytic functions. This distinguishes the analytic case from the case of finite smoothness.

Article (Russian)

On one approach to the discretization of the lavrent’ev method

Pereverzev S. V., Solodkii S. G.

↓ Abstract | Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 212-219

We propose a new scheme of discretization of the Lavrent’ev method for operator equations of the first kind with self-adjoint nonnegative operators of certain “smoothness.” This scheme is more economical in the sense of the amount of used discrete information as compared with traditional approaches.

Article (Ukrainian)

Optimal rates of convergence of some iterative approximation methods for the solution of fredholm equations in spaces of periodic analytic functions

Askarov M., Pereverzev S. V.

↓ Abstract | Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 9. - pp. 1208–1215

We consider some classes of Fredholm equations with integral operators acting in spaces of periodic analytic functions. For these classes, we establish the exact order of the optimal rates of convergence for some versions of the method of iterative projections and KP methods.

Article (Ukrainian)