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 Mat. Zametki, 2016, Volume 99, Issue 1, Pages 26–34 (Mi mz10852)

An Algorithm for Constructing Multidimensional Continued Fractions and Linear Dependence of Numbers

E. B. Borodina

Lomonosov Moscow State University

Abstract: The Güting algorithm for constructing multidimensional continued fractions is considered. It is proved that, in the case of dimension $2$, this algorithm can be used to find the coefficients of the linear dependence of numbers; a criterion is given for verifying that the partial quotients furnished by the algorithm are, indeed, elements of the continued fraction for the expanded (generally irrational) numbers.

Keywords: multidimensional continued fraction, Güting algorithm, linear dependence of numbers, partial quotient, irrational number.

 Funding Agency Grant Number Russian Foundation for Basic Research 09-01-00743

DOI: https://doi.org/10.4213/mzm10852

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English version:
Mathematical Notes, 2016, 99:1, 37–45

Bibliographic databases:

UDC: 511
Revised: 17.06.2015

Citation: E. B. Borodina, “An Algorithm for Constructing Multidimensional Continued Fractions and Linear Dependence of Numbers”, Mat. Zametki, 99:1 (2016), 26–34; Math. Notes, 99:1 (2016), 37–45

Citation in format AMSBIB
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