Chebyshev polynomials involved in the Householder's method for square roots
General Mathematics
2025-01-10 v1
Abstract
The Householder's method is a root-find algorithm which is a natural extension of the methods of Newton and Halley. The current paper mostly focuses on approximating the square root of a positive real number based on these methods. The resulting algorithms can be expressed using Chebyshev polynomials. An extension to the nth root is also proposed.
Keywords
Cite
@article{arxiv.2501.04703,
title = {Chebyshev polynomials involved in the Householder's method for square roots},
author = {Yann Dijoux},
journal= {arXiv preprint arXiv:2501.04703},
year = {2025}
}
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