L-Algorithm for Approximation of Diophantine Systems of Linear Forms

An L -algorithm is proposed for constructing an infinite sequence of integer solutions to systems of linear inequalities in d + 1 variables. The solutions are obtained using recurrence relations of order d + 1. The approximation rate is estimated by the Diophantine exponent θ = m n − ϱ , where 1 ≤ n...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2022-03, Vol.261 (4), p.517-533
Main Author: Zhuravlev, V. G.
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Inequalities
Linear functions
Mathematical analysis
Mathematics
Mathematics and Statistics
Online Access:Get full text
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Summary:An L -algorithm is proposed for constructing an infinite sequence of integer solutions to systems of linear inequalities in d + 1 variables. The solutions are obtained using recurrence relations of order d + 1. The approximation rate is estimated by the Diophantine exponent θ = m n − ϱ , where 1 ≤ n ≤ d is the number of inequalities, m = d + 1 − n is the number of free variables, and the deviation ϱ  > 0 can be made arbitrarily small due to a suitable choice of the recurrence relation.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-05766-3