Linear-Fractional Invariance of the Simplex-Module Algorithm for Expanding Algebraic Numbers in Multidimensional Continued Fractions

The paper establishes the invariance of the simplex-module algorithm for expanding real numbers α  = ( α 1 , …,  α d ) in multidimensional continued fractions under linear-fractional transformations α ′ = α 1 ′ … α d 1 = U α with matrices U from the unimodular group GL d +1 (ℤ). It is shown that the...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2018-11, Vol.234 (5), p.640-658
Main Author: Zhuravlev, V. G.
Format: Article
Language:English
Subjects:
Algorithms
Mathematics
Mathematics and Statistics
Statistics
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Summary:The paper establishes the invariance of the simplex-module algorithm for expanding real numbers α  = ( α 1 , …,  α d ) in multidimensional continued fractions under linear-fractional transformations α ′ = α 1 ′ … α d 1 = U α with matrices U from the unimodular group GL d +1 (ℤ). It is shown that the convergents of the transformed collections of numbers α ′ satisfy the same recurrence relation and have the same approximation order.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-018-4034-3