Proceedings of the Steklov Institute of Mathematics

, Volume 299, Issue 1, pp 268–287 | Cite as

Simplex—Karyon Algorithm of Multidimensional Continued Fraction Expansion

  • V. G. Zhuravlev


A simplex–karyon algorithm for expanding real numbers α = (α1,..., α d ) in multidimensional continued fractions is considered. The algorithm is based on a (d + 1)-dimensional superspace S with embedded hyperplanes: a karyon hyperplane K and a Farey hyperplane F. The approximation of numbers α by continued fractions is performed on the hyperplane F, and the degree of approximation is controlled on the hyperplane K. A local ℘(r)-strategy for constructing convergents is chosen, with a free objective function ℘(r) on the hyperplane K.


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© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Vladimir State University Named after Alexander and Nikolay StoletovsVladimirRussia

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