Convergence speed of the Brun algorithm over formal power series field

Amara Chandoul ()
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Amara Chandoul: Higher Institute of Informatics and Multimedia of Sfax

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 1, 390-403

Abstract: Abstract We study multidimensional continued fraction algorithms throughout the field of formal power series. In this case, we establish a relation between the Jacobi-Perron algorithm and the version of it introduced by Dubois. Regarding the periodicity of the Jacobi-Perron algorithm, we define periodic vectors whose coordinates belong to certain finite degree extension fields. We prove also that the convergence of Brun algorithm in the case of multidimensional continued fractions over the Field of Formal Power Series is not exponential.

Keywords: Convergence speed; Multidimensional continued fractions; Brun algorithm; Jacobi–Perron algorithm; Field of Formal Power Series (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-023-00488-x

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