On Optimal Recovery and Information Complexity in Numerical Differentiation and Summation
Numerical Analysis
2024-11-12 v2 Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2405.20020,
title = {On Optimal Recovery and Information Complexity in Numerical Differentiation and Summation},
author = {Y. V. Semenova and S. G. Solodky},
journal= {arXiv preprint arXiv:2405.20020},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:2309.05425, arXiv:2309.09710