Polynomial degree reduction in the $\mathcal{L}^2$-norm on a symmetric interval for the canonical basis
Numerical Analysis
2022-03-08 v1 Numerical Analysis
Abstract
In this paper, we develop a direct formula for determining the coefficients in the canonical basis of the best polynomial of degree that approximates a polynomial of degree on a symmetric interval for the -norm. We also formally prove that using the formula is more computationally efficient than using a classical matrix multiplication approach and we provide an example to illustrate that it is more numerically stable than the classical approach.
Cite
@article{arxiv.2105.07258,
title = {Polynomial degree reduction in the $\mathcal{L}^2$-norm on a symmetric interval for the canonical basis},
author = {Habib Ben Abdallah and Christopher J. Henry and Sheela Ramanna},
journal= {arXiv preprint arXiv:2105.07258},
year = {2022}
}