Pereverzev S. V.
Optimal discretization of Ill-posed problems
Pereverzev S. V., Solodkii S. G.
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.
On the optimization of projection-iterative methods for the approximate solution of ill-posed problems
Pereverzev S. V., Solodkii S. G.
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.
Optimal methods for specifying information in the solution of integral equations with analytic kernels
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.
On one approach to the discretization of the lavrent’ev method
Pereverzev S. V., Solodkii S. G.
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.
On direct methods for solution of regularized equations
Pereverzev S. V., Solodkii S. G.
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.
On the rate of convergence of projection-iterative methods for classes of weakly singular integral equations
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.
Information complexity of weakly singular integral equations
Makhkamov K. Sh., Pereverzev S. V.
Ukr. Mat. Zh. - 1994. - 46, № 11. - pp. 1527–1533
We establish the exact power order of information complexity for integral equations whose kernels have power singularities and free terms belong to the corresponding Hölder space.
Optimal rates of convergence of some iterative approximation methods for the solution of fredholm equations in spaces of periodic analytic functions
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.
Galerkin information, the hyperbolic cross, and the complexity of operator equations
Makhkamov K. Sh., Pereverzev S. V.
Ukr. Mat. Zh. - 1991. - 43, № 5. - pp. 639–648
An estimate of the complexity of the approximate solution of fredholm equations of the second kind with differentiable kernels
Ukr. Mat. Zh. - 1989. - 41, № 10. - pp. 1422–1425
Complexity of the problem of finding the solutions of fredholm equations of the second kind with smooth kernels. I
Ukr. Mat. Zh. - 1988. - 40, № 1. - pp. 84-91
A problem of approximate integration, arising in the theory of queueing systems
Myrzanov Zh. E., Pereverzev S. V.
Ukr. Mat. Zh. - 1987. - 39, № 5. - pp. 598–602
Approximation numbers and approximation of the eigenvalues of integral operators
Ukr. Mat. Zh. - 1987. - 39, № 2. - pp. 204-209
Optimal methods of prescribing information for the solution of integral equations with differentiate kernels
Ukr. Mat. Zh. - 1986. - 38, № 1. - pp. 55–63
Rate of convergence of the Sokolov-type methods for integral equations with differentiable kernels
Ukr. Mat. Zh. - 1985. - 37, № 5. - pp. 605–609
A problem concerning the optimization of the methods for approximate solution of Fredholm equations
Ukr. Mat. Zh. - 1983. - 35, № 3. - pp. 378 — 382
Orderwise optimal methods of approximate solution of Fredholm integral equations
Ukr. Mat. Zh. - 1980. - 32, № 2. - pp. 181 - 188
Exact values of approximation by hermitian splines on a class of functions of two variables
Ukr. Mat. Zh. - 1979. - 31, № 5. - pp. 510–516