Abstract
Barycentric interpolation, which comes from Lagrange interpolation, is a useful method in numerical analysis. In this research paper, we explain how the barycentric interpolation formula is derived and discuss its features. We compare its stability and performance with the traditional Lagrange formula. First, we show how to get the barycentric formula from the Lagrange polynomial and present it as a rational function. We also provide an estimate of the error. Then, we use numerical examples to show that the barycentric formula is more stable and works better, especially when the degree of interpolation is high. Our results show that the barycentric method stays stable and gives smaller errors than the Lagrange method. This paper helps improve the understanding of how strong and reliable the barycentric method is, and how it can be better than older methods in numerical analysis. In particular, the novelty of this work lies in presenting a structured error analysis based on Legendre nodes and validating the stability of barycentric interpolation through comparison across four distinct classes of test functions.
Recommended Citation
Yawar, Alvira and Bahadur, Swarnima
(2025).
(R2151) Error Estimates of Barycentric Lagrange Interpolation,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 20,
Iss.
2, Article 7.
Available at:
https://digitalcommons.pvamu.edu/aam/vol20/iss2/7