An improved bound on Legendre approximation
Numerical Analysis
2022-07-28 v1 Numerical Analysis
Abstract
In this paper, new relations between the derivatives of the Legendre polynomials are obtained, and by these relations, new upper bounds for the Legendre coefficients of differentiable functions are presented. These upper bounds are sharp and cover more categories of differentiable functions. Moreover, new and sharper bounds for the approximation error of the partial sums of Legendre polynomials are provided. Numerical examples are given to validate our theoretical results.
Cite
@article{arxiv.2207.13477,
title = {An improved bound on Legendre approximation},
author = {M. Hamzehnejad and M. M. Hosseini and A. Salemi},
journal= {arXiv preprint arXiv:2207.13477},
year = {2022}
}
Comments
The paper contains 15 pages