Vandermonde with Arnoldi
Numerical Analysis
2019-11-25 v1 Numerical Analysis
Abstract
Vandermonde matrices are exponentially ill-conditioned, rendering the familiar "polyval(polyfit)" algorithm for polynomial interpolation and least-squares fitting ineffective at higher degrees. We show that Arnoldi orthogonalization fixes the problem.
Cite
@article{arxiv.1911.09988,
title = {Vandermonde with Arnoldi},
author = {Pablo D. Brubeck and Yuji Nakatsukasa and Lloyd N. Trefethen},
journal= {arXiv preprint arXiv:1911.09988},
year = {2019}
}