On efficient approximation of quadratic irrationals
Number Theory
2025-12-01 v2
Abstract
We provide efficient algorithms to compute convergents of quadratic irrationals. We show that for square roots, provided Galois' refinement of Lagrange's theorem holds, certain decimations of the sequence of convergents are signed Chebyshev sequences, which can be also be generated by a Householder method.
Cite
@article{arxiv.2511.21617,
title = {On efficient approximation of quadratic irrationals},
author = {Peter H. van der Kamp and Anthony Overmars and Marcel Jackson and Andrew Hone},
journal= {arXiv preprint arXiv:2511.21617},
year = {2025}
}
Comments
14 pages, no figures