Polynomial interpolation in the monomial basis is stable after all

12/20/2022

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by   Zewen Shen, et al.

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Polynomial interpolation in the monomial basis is often considered to be a bad idea in numerical computations. In this paper, we show that this belief is wrong, in the sense that, despite the ill-conditioning of the Vandermonde matrix, polynomial interpolation in the monomial basis is as accurate as polynomial interpolation in a more well-conditioned basis in many cases of interest. Furthermore, we show that the monomial basis is superior to other polynomial bases in a number of applications.