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The numerical stability of barycentric Lagrange interpolation
Abstract
The Lagrange representation of the interpolating polynomial can be rewritten in two\nmore computationally attractive forms: a modified Lagrange form and a barycentric\nform. We give an error analysis of the evaluation of the interpolating polynomial using\nthese two forms. The modified Lagrange formula is shown to be backward stable. The\nbarycentric formula has a less favourable error analysis, but is forward stable for any set of\ninterpolating points with a small Lebesgue constant. Therefore the barycentric formula can\nbe significantly less accurate than the modified Lagrange formula only for a poor choice of\ninterpolating points. This analysis provides further weight to the argument of Berrut and\nTrefethen that barycentric Lagrange interpolation should be the polynomial interpolation\nmethod of choice.
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Cited by
Barycentric Lagrange Interpolation
Berrut, J.-P., & Trefethen, L. N. (2004) · SIAM Review · doi:10.1137/s0036144502417715 · Cited by 1,245
The spectra of gravitational atoms
Baumann, D., Chia, H. S., Stout, J., & Haar, L. T. (2019) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2019/12/006 · Cited by 194
Metadata
- Authors
- Higham, N. J.
- Venue
- IMA Journal of Numerical Analysis
- Publisher
- Oxford University Press (OUP)
- Published
- 2004-10-01
- Volume
- 24
- Issue
- 4
- Pages
- 547-556
- ISSN
- 0272-4979 (ISSN-L)
- 1464-3642
- OpenAlex
- W2056522847
- Cited by
- 343
- References
- 0
- FWCI
- 14.53
- Type
- journal article
- Language
- en
- Open access
- closed
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- Higham, N. J. (2004). The numerical stability of barycentric Lagrange interpolation. IMA Journal of Numerical Analysis. https://doi.org/10.1093/imanum/24.4.547
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