On efficient approximation of quadratic irrationals
classification
🧮 math.NT
keywords
convergentsefficientirrationalsquadraticalgorithmsapproximationcertainchebyshev
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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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