A new and sharper bound for Legendre expansion of differentiable functions
Numerical Analysis
2018-06-18 v1
Abstract
In this paper, we provide a new and sharper bound for the Legendre coefficients of differentiable functions and then derive a new error bound of the truncated Legendre series in the uniform norm. The key idea of proof relies on integration by parts and a sharp Bernstein-type inequality for the Legendre polynomial. An illustrative example is provided to demonstrate the sharpness of our new results.
Keywords
Cite
@article{arxiv.1803.00336,
title = {A new and sharper bound for Legendre expansion of differentiable functions},
author = {Haiyong Wang},
journal= {arXiv preprint arXiv:1803.00336},
year = {2018}
}
Comments
9pages