Khlobystov V. V.
Ukr. Mat. Zh. - 2010. - 62, № 4. - pp. 494–503
We establish conditions for the existence of continual nodes for interpolation polynomials of the integral type. This result is generalized to the case of multivariable operators. Some examples of these interpolants are analyzed.
Ukr. Mat. Zh. - 2006. - 58, № 4. - pp. 554–563
In a Hilbert space, we construct an interpolation approximation of the Taylor polynomial for differentiable operators. By using this approximation, we obtain estimates of accuracy for analytic operators that strengthen previously known results and for operators containing finitely many Fréchet derivatives.
Analysis of the Accuracy of Interpolation of Entire Operators in a Hilbert Space in the Case of Perturbed Nodal Values
Ukr. Mat. Zh. - 2003. - 55, № 7. - pp. 953-960
In a Hilbert space with Gaussian measure, we obtain an estimate for the accuracy of interpolation of an entire operator in the case where its values are perturbed at nodes and determine the value of the degree of an interpolation polynomial the exceeding of which does not improve the estimate of the accuracy of interpolation.
Ukr. Mat. Zh. - 2003. - 55, № 6. - pp. 779-789
We construct an integral Newton-type interpolation polynomial with a continual set of nodes. This interpolant is unique and preserves an operator polynomial of the corresponding degree.
Ukr. Mat. Zh. - 2003. - 55, № 4. - pp. 479-488
For nonlinear functionals defined on the space of piecewise-continuous functions, we construct an interpolational integral continued fraction on continual piecewise-continuous nodes and establish conditions for the existence and uniqueness of interpolants of this type.
Ukr. Mat. Zh. - 1991. - 43, № 10. - pp. 1361–1368