English

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}
}

Comments

Under Submission

R2 v1 2026-06-28T21:00:12.372Z