On polynomial interpolation in the monomial basis

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.

31 pages, 17 figures. Accepted by SIAM J. Numer. Anal

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Cited by in corpus (1)

• The numerical linear algebra of weights: from the spectral analysis to conditioning and preconditioning in the Laplacian case