2019
Том 71
№ 7

All Issues

Zhuk P. F.

Articles: 3
Article (Russian)

Asymptotic Rate of Convergence of a Two-Layer Iterative Method of the Variational Type

Musina A. A., Zhuk P. F.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 12. - pp. 1622–1635

We present the definition and study the dependence on the initial approximation of the asymptotic rate of convergence of a two-layer symmetrizable iterative method of the variational type. The explicit expression is obtained for the substantial (with respect to the Lebesgue measure) range of its values. Its domain of continuity is described.

Brief Communications (Russian)

Exact estima tes for the rate of convergence of the s-step method of steepest descent in eigenvalue problems

Bondarenko L. N., Zhuk P. F.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 12. - pp. 1694–1699

We obtain exact (unimprovable) estimates for the rate of convergence of the s-step method of steepest descent for finding the least (greatest) eigenvalue of a linear bounded self-adjoint operator in a Hilbert space.

Article (Ukrainian)

Convergence rate of Kantorovich's method for nonlinear differential equations

Zhuk P. F.

Full text (.pdf)

Ukr. Mat. Zh. - 1976. - 28, № 2. - pp. 183–193