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IMA Journal of Numerical Analysis 2004 24(4):547-556; doi:10.1093/imanum/24.4.547
© 2004 by Institute of Mathematics and its Applications
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The numerical stability of barycentric Lagrange interpolation

Nicholas J. Higham1

1 Department of Mathematics, University of Manchester, Manchester M13 9PL, UK

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.

Key Words: polynomial interpolation; Lagrange interpolation; barycentric formula; rounding error analysis; backward error; forward error; Lebesgue constant

Received 4 December 2003. Revised 4 February 2004.


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