arXiv subjects

Y. V. Semenova

Publications and source records attributed to Y. V. Semenova.

4 recordsLinked to original sources

arXiv2024

On Optimal Recovery and Information Complexity in Numerical Differentiation and Summation

In this paper, we study optimization problems of numerical differentiation and summation methods on classes of univariate functions. Sharp estimates (in order) of the optimal recovery error and information complexity are calculated for these classes. Algorithms are constructed based on the truncation method and Chebyshev polynomials to implement these estimates. Moreover, we establish under what conditions the summation problem is well-posed.

math.NA↗

arXiv2024

An optimal method for high order mixed derivatives of bivariate functions

The problem of optimal recovering high-order mixed derivatives of bivariate functions with finite smoothness is studied. Based on the truncation method, an algorithm for numerical differentiation is constructed, which is order-optimal both in the sense of accuracy and in terms of the amount of involved Galerkin information. Numerical examples are provided to illustrate the fact that our approach can be implemented successfully.

math.NA↗

arXiv2023

About optimization of methods for mixed derivatives of bivariate functions

The problem of optimal recovering high-order mixed derivatives of bivariate functions with finite smoothness is studied. On the basis of the truncation method, an algorithm for numerical differentiation is constructed, which is order-optimal both in the sense of accuracy and in terms of the amount of involved Galerkin information.

math.NA↗

arXiv2023

On optimal recovering high order partial derivatives of bivariate functions

The problem of recovering partial derivatives of high orders of bivariate functions with finite smoothness is studied. Based on the truncation method, a numerical differentiation algorithm was constructed, which is optimal by the order, both in the sense of accuracy and in the sense of the amount of Galerkin information involved. Numerical demonstrations are provided to illustrate that the proposed method can be implemented successfully.

math.NA↗