The numerical stability of barycentric Lagrange interpolation

Higham, Nicholas J (2004) The numerical stability of barycentric Lagrange interpolation. IMA Journal of Numerical Analysis, 24. pp. 547-556. ISSN 1464-3642

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Abstract

The Lagrange representation of the interpolating polynomial can be rewritten in two more computationally attractive forms: a modified Lagrange form and a barycentric form. We give an error analysis of the evaluation of the interpolating polynomial using these two forms. The modified Lagrange formula is shown to be backward stable. The barycentric formula has a less favourable error analysis, but is forward stable for any set of interpolating points with a small Lebesgue constant. Therefore the barycentric formula can be significantly less accurate than the modified Lagrange formula only for a poor choice of interpolating points. This analysis provides further weight to the argument of Berrut and Trefethen that barycentric Lagrange interpolation should be the polynomial interpolation method of choice.

Item Type:	Article
Uncontrolled Keywords:	Keywords: polynomial interpolation; Lagrange interpolation; barycentric formula; rounding error analysis; backward error; forward error; Lebesgue constant.
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User:	Ms Lucy van Russelt
Date Deposited:	27 Jun 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/315

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