Computational and Applied Mathematics

, Volume 37, Issue 3, pp 3539–3561 | Cite as

Weak and strong orders of linear recurring sequences

  • Zenonas Navickas
  • Minvydas Ragulskis
  • Dovile Karaliene
  • Tadas Telksnys


The concept of the strong order of linear recurring sequence (LRS) is introduced in this paper. Necessary and sufficient conditions for the existence of the strong LRS order are derived. The strong LRS order is exploited for the formalization of the problem of the extension of a sequence from the available fragment (fragments) of that sequence. The definition of the strong LRS order opens new possibilities for formal sequence analysis whenever the weak LRS order of that sequence exists. Computational experiments with discrete iterative maps are used to illustrate the applicability of the strong LRS order in nonlinear system analysis.


Linear recurring sequence Strong and weak orders Sequence extrapolation 

Mathematics Subject Classification

65Q30 37M10 37G35 



This research was funded by a Grant (No. MIP078/15) from the Research Council of Lithuania.


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017

Authors and Affiliations

  1. 1.Department of Mathematical ModelingKaunas University of TechnologyKaunasLithuania
  2. 2.Research Group for Mathematical and Numerical Analysis of Dynamical SystemsKaunas University of TechnologyKaunasLithuania
  3. 3.Department of Applied MathematicsKaunas University of TechnologyKaunasLithuania

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