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arXiv · 2511.21617

On efficient approximation of quadratic irrationals, signed Chebyshev polynomials and Householder's method

Peter H. van der Kamp·Anthony Overmars·Marcel Jackson·Andrew N. W. Hone
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Abstract

We provide efficient algorithms to compute convergents of quadratic irrationals. We show that for square roots, in settings where 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.

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Peter H. van der Kamp, Anthony Overmars, Marcel Jackson, Andrew N. W. Hone. 2026-09-04. On efficient approximation of quadratic irrationals, signed Chebyshev polynomials and Householder's method. https://arxiv.org/abs/2511.21617

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