The numerical stability of barycentric Lagrange interpolation

@inproceedings{Higham2003TheNS,
  title={The numerical stability of barycentric Lagrange interpolation},
  author={Nicholas J. Higham},
  year={2003}
}
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… CONTINUE READING