2019
Том 71
№ 6

All Issues

Pereverzev S. V.

Articles: 17
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)

On the optimization of projection-iterative methods for the approximate solution of ill-posed problems

Pereverzev S. V., Solodkii S. G.

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Ukr. Mat. Zh. - 1996. - 48, № 11. - pp. 1530-1537

We consider a new version of the projection-iterative method for the solution of operator equations of the first kind. We show that it is more economical in the sense of amount of used discrete information.

Article (Russian)

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

Azizov M., Pereverzev S. V.

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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 (Russian)

On direct methods for solution of regularized equations

Pereverzev S. V., Solodkii S. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1995. - 47, № 9. - pp. 1231–1242

We prove that the application of so-called adaptive direct methods to approximation of Fredholm equations of the first kind leads to a more economical way of finite-dimensional approximation as compared with traditional approaches.

Article (Russian)

On the rate of convergence of projection-iterative methods for classes of weakly singular integral equations

Askarov M., Pereverzev S. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1995. - 47, № 4. - pp. 498–505

For classes of weakly singular integral equations of the second kind whose kernels have a power singularity, we find the optimal order of the rate of convergence of projection-iterative methods. Moreover, iterative methods of the Sokolov type are considered and, for weakly singular equations with differentiable coefficients, we present estimates of the rate of convergence of such methods.

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)

Galerkin information, the hyperbolic cross, and the complexity of operator equations

Makhkamov K. Sh., Pereverzev S. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1991. - 43, № 5. - pp. 639–648

Article (Ukrainian)

An estimate of the complexity of the approximate solution of fredholm equations of the second kind with differentiable kernels

Pereverzev S. V.

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Ukr. Mat. Zh. - 1989. - 41, № 10. - pp. 1422–1425

Article (Ukrainian)

Complexity of the problem of finding the solutions of fredholm equations of the second kind with smooth kernels. I

Pereverzev S. V.

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Ukr. Mat. Zh. - 1988. - 40, № 1. - pp. 84-91

Article (Ukrainian)

A problem of approximate integration, arising in the theory of queueing systems

Myrzanov Zh. E., Pereverzev S. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1987. - 39, № 5. - pp. 598–602

Article (Ukrainian)

Approximation numbers and approximation of the eigenvalues of integral operators

Pereverzev S. V.

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Ukr. Mat. Zh. - 1987. - 39, № 2. - pp. 204-209

Article (Ukrainian)

Optimal methods of prescribing information for the solution of integral equations with differentiate kernels

Pereverzev S. V.

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Ukr. Mat. Zh. - 1986. - 38, № 1. - pp. 55–63

Article (Ukrainian)

Rate of convergence of the Sokolov-type methods for integral equations with differentiable kernels

Pereverzev S. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1985. - 37, № 5. - pp. 605–609

Article (Ukrainian)

A problem concerning the optimization of the methods for approximate solution of Fredholm equations

Pereverzev S. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1983. - 35, № 3. - pp. 378 — 382

Article (Ukrainian)

Orderwise optimal methods of approximate solution of Fredholm integral equations

Pereverzev S. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1980. - 32, № 2. - pp. 181 - 188

Article (Ukrainian)

Exact values of approximation by hermitian splines on a class of functions of two variables

Pereverzev S. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1979. - 31, № 5. - pp. 510–516