A new multidimensional continued fraction algorithm

DOI10.1090/S0025-5718-09-02217-0zbMath1217.11067OpenAlexW1984386996MaRDI QIDQ3055196

Shin-ichi Yasutomi, Jun-ichi Tamura

Publication date: 7 November 2010

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-09-02217-0

zbMATH Keywords

periodic continued fractionmodified Jacobi-Perron algorithmalgorithms of continued fraction expansions

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) Cubic and quartic extensions (11R16) Continued fraction calculations (number-theoretic aspects) (11Y65)

Related Items (7)

Pseudorandom number generation using chaotic true orbits of the Bernoulli map ⋮ Linear recurrence sequences and periodicity of multidimensional continued fractions ⋮ Numeration and discrete dynamical systems ⋮ On the finiteness and periodicity of the 𝑝-adic Jacobi–Perron algorithm ⋮ On $p$-adic multidimensional continued fractions ⋮ A New Multidimensional Slow Continued Fraction Algorithm and Stepped Surface ⋮ On the periodic writing of cubic irrationals and a generalization of Rédei functions

Cites Work

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• On simultaneous approximation to \((\alpha,\alpha^2)\) with \(\alpha^3+k\alpha-1=0\).
• The Jacobi-Perron algorithm its theory and application
• A class of transcendental numbers having explicit g-adic and Jacobi-Perron expansions of arbitrary dimension
• On almost everywhere exponential convergence of the modified Jacobi-Perron algorithm: a corrected proof
• Numerische Ergebnisse zum JACOBIschen Kettenbruchalgorithmus in rein‐kubischen Zahlkörpern

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