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arXiv · 2501.04703

Chebyshev polynomials involved in the Householder's method for square roots

Yann Dijoux
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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.

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Yann Dijoux. 2024-12-11. Chebyshev polynomials involved in the Householder's method for square roots. https://arxiv.org/abs/2501.04703

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