The Laurent-Horner method for validated evaluation of Chebyshev expansions
Numerical Analysis
2024-09-24 v1 Numerical Analysis
Abstract
We develop a simple two-step algorithm for enclosing Chebyshev expansions whose cost is linear in terms of the polynomial degree. The algorithm first transforms the expansion from Chebyshev to the Laurent basis and then applies the interval Horner method. It outperforms the existing eigenvalue-based methods if the degree is high or the evaluation point is close to the boundaries of the domain.
Keywords
Cite
@article{arxiv.2409.14952,
title = {The Laurent-Horner method for validated evaluation of Chebyshev expansions},
author = {Jared L. Aurentz and Behnam Hashemi},
journal= {arXiv preprint arXiv:2409.14952},
year = {2024}
}