2019
Том 71
№ 11

# Urumbaev A. N.

Articles: 3
Article (Russian)

### On finite-dimensional approximation of solutions of ill-posed problems

Ukr. Mat. Zh. - 1997. - 49, № 2. - pp. 289–295

We show that the modified method for finite-dimensional approximation of solutions of Fredholm integral equations of the first kind presented in this paper is more economical than traditional methods for finite-dimensional approximation.

Article (Ukrainian)

### Optimization of direct methods for the approximate solution of weakly singular integral equations

Ukr. Mat. Zh. - 1994. - 46, № 9. - pp. 1246–1254

For a class of weakly singular integral equations with power and logarithmic singularities, we establish the optimal order of the error of direct methods and indicate the procedure which realizes this order.

Article (Russian)

### On the optimization of direct methods for solving fredholm integral equations of the second kind with infinitely smooth kernels

Ukr. Mat. Zh. - 1993. - 45, № 12. - pp. 1695–1701

We give a direct method, optimal in $L_2$, for solving the Fredholm integral equation of the second kind with operators acting into the space of functions harmonic in a disk or into the space of functions that can be analytically extended to an infinite strip. The exact order of the error of this method is determined.