arXiv subjects

Anthony Overmars

Publications and source records attributed to Anthony Overmars.

2 recordsLinked to original sources

arXiv2025

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

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.

math.NT↗

arXiv2015

A new parameterisation of Pythagorean triples in terms of odd and even series

In this paper we introduce a formula that parameterises the Pythagorean triples as elements of two series. With respect to the standard Euclidean formula, this parameterisation does not generate the Pythagorean triples where the elements of the triple are all divisible by 2. A necessary and sufficient condition is also proposed for a Pythagorean triple obtained from this formula to be primitive.

math.HO↗