Selmer's Multiplicative Algorithm

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The behavior of the multiplicative acceleration of Selmer’s algorithm is widely unknown and no general result on convergence has been detected yet. Solely for its 2-dimensional, periodic expansions, there exist some results on convergence and approximation due to Fritz Schweiger. In this paper we show that periodic expansions of any dimension do in fact converge and that the coordinates of the limit points are rational functions of the largest eigenvalue of the periodicity matrix.
Original languageEnglish
Pages (from-to)1-20
Number of pages20
Publication statusPublished - 2011
Externally publishedYes


  • multidimensional continued fractions
  • Selmer
  • Periodic expansions

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