English

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 MM that approximates a polynomial of degree N>MN>M on a symmetric interval for the L2\mathcal{L}^2-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.

Keywords

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}
}