English

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}
}
R2 v1 2026-06-23T12:24:25.594Z