Geodesic
An Algorithm for Constructing Multidimensional Continued Fractions and Linear Dependence of Numbers
Matematičeskie zametki, Tome 99 (2016) no. 1, pp. 26-34

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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, irrational number.
Mots-clés : partial quotient 
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     author = {E. B. Borodina},
     title = {An {Algorithm} for {Constructing} {Multidimensional} {Continued} {Fractions} and {Linear} {Dependence} of {Numbers}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {26--34},
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     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_1_a2/}
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E. B. Borodina. An Algorithm for Constructing Multidimensional Continued Fractions and Linear Dependence of Numbers. Matematičeskie zametki, Tome 99 (2016) no. 1, pp. 26-34. http://geodesic.mathdoc.fr/item/MZM_2016_99_1_a2/