On polynomial interpolation in the monomial basis
Numerical Analysis
2025-03-06 v5 Numerical Analysis
Abstract
In this paper, we show that the monomial basis is generally as good as a well-conditioned polynomial basis for interpolation, provided that the condition number of the Vandermonde matrix is smaller than the reciprocal of machine epsilon. This leads to a practical algorithm for piecewise polynomial interpolation over general regions in the complex plane using the monomial basis. Our analysis also yields a new upper bound for the condition number of an arbitrary Vandermonde matrix, which generalizes several previous results.
Cite
@article{arxiv.2212.10519,
title = {On polynomial interpolation in the monomial basis},
author = {Zewen Shen and Kirill Serkh},
journal= {arXiv preprint arXiv:2212.10519},
year = {2025}
}
Comments
31 pages, 17 figures. Accepted by SIAM J. Numer. Anal