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arXiv · 2212.10519

On polynomial interpolation in the monomial basis

Zewen Shen·Kirill Serkh
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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.

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Zewen Shen, Kirill Serkh. 2025-02-24. On polynomial interpolation in the monomial basis. https://doi.org/10.1137/23m1623215

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