Software implementation of parallel matrix computations for linear recurrent sequence and numerical methods for estimating its efficiency

Abstract The possibility to generalize the notion of a linear recurrent sequence (LRS) over a commutative ring to the case of a LRS over a non-commutative ring is discussed. In this context, an arbitrary bimodule AMB over left- and right-Artinian rings A and B, respectively, is associated with the equivalent bimodule of translations CMZ, where C is the multiplicative ring of the bimodule AMB and Z is its center, and the relation between the quasi-Frobenius conditions for the bimodules AMB and CMZ is studied. It is demonstrated that, in the general case, the fact that AMB is a quasi-Frobenius bimodule does not imply the validity of the quasi-Frobenius condition for the bimodule CMZ. However, under some additional assumptions it can be shown that if CMZ is a quasi-Frobenius bimodule, then the bimodule AMB is quasi-Frobenius as well.

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The presence of a zero in an integer linear recurrent sequence is NP-hard to decide

Linear Algebra and its Applications ◽

10.1016/s0024-3795(01)00466-9 ◽

2002 ◽

Vol 351-352 ◽

pp. 91-98 ◽

Cited By ~ 18

Author(s):

Vincent D. Blondel ◽

Natacha Portier

Keyword(s):

Np Hard ◽

Recurrent Sequence ◽

Linear Recurrent Sequence

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Nonlinear Filtration Algorithms of Binary Linear Recurrent Sequence with Random Delay and Random Initial Phase

2019 Systems of Signal Synchronization, Generating and Processing in Telecommunications (SYNCHROINFO) ◽

10.1109/synchroinfo.2019.8814282 ◽

2019 ◽

Author(s):

M. G. Bakulin ◽

V. B. Kreyndelin ◽

D. Yu. Pankratov

Keyword(s):

Initial Phase ◽

Nonlinear Filtration ◽

Random Delay ◽

Recurrent Sequence ◽

Linear Recurrent Sequence ◽

Filtration Algorithms

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Effective numerical methods to model dynamic behavior of springs with torsion

10.32469/10355/66377 ◽

2018 ◽

Author(s):

◽

E. Dilan Fernando

Keyword(s):

Numerical Methods ◽

Differential Equations ◽

Numerical Method ◽

Dynamic Behavior ◽

Numerical Models ◽

Software Implementation ◽

Computer Language ◽

Newtonian Mechanics ◽

Systems Of Differential Equations ◽

Kirchhoff Problem

The purpose of this thesis is to find effective algorithms to numerically solve certain systems of differential equations that arise from standard Newtonian mechanics. Numerical models of elastica has already been well studied. In this thesis we concentrate on the Kirchhoff problem. The goal is to create an effective and robust numerical method to model the dynamic behavior of springs that have a prescribed natural curvature. In addition to the mathematics, we also provide the implementation details of the numerical method using the computer language Python 3. We also discuss in detail the various difficulties of such a software implementation and how certain auxiliary computations can make the software more effective and robust.

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Iteration of the modular period of a second order linear recurrent sequence

Acta Arithmetica ◽

10.4064/aa-22-3-249-256 ◽

1973 ◽

Vol 22 (3) ◽

pp. 249-256

Author(s):

Donald Robinson

Keyword(s):

Second Order ◽

Recurrent Sequence ◽

Order Linear ◽

Linear Recurrent Sequence

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On the Constant in the Average Digit Sum for a Recurrence-Based Numeration

Uniform distribution theory ◽

10.1515/udt-2016-0016 ◽

2016 ◽

Vol 11 (2) ◽

pp. 125-150

Author(s):

Christian Ballot

Keyword(s):

Positive Constant ◽

Asymptotic Result ◽

Elementary Approach ◽

Recurrent Sequence ◽

Explicit Formulas ◽

Large Classes ◽

Initial Term ◽

Linear Recurrent Sequence ◽

Positive Integers ◽

The Greedy Algorithm

AbstractGiven an integral, increasing, linear-recurrent sequence A with initial term 1, the greedy algorithm may be used on the terms of A to represent all positive integers. For large classes of recurrences, the average digit sum is known to equal cA log n+O(1), where cA is a positive constant that depends on A. This asymptotic result is re-proved with an elementary approach for a class of special recurrences larger than, or distinct from, that of former papers. The focus is on the constants cA for which, among other items, explicit formulas are provided and minimal values are found, or conjectured, for all special recurrences up to a certain order.

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An extended Prony’s interpolation scheme on an equispaced grid

Open Mathematics ◽

10.1515/math-2015-0031 ◽

2015 ◽

Vol 13 (1) ◽

Cited By ~ 1

Author(s):

Dovile Karalienė ◽

Zenonas Navickas ◽

Raimondas Čiegis ◽

Minvydas Ragulskis

Keyword(s):

Interpolation Scheme ◽

Recurrent Sequence ◽

Minimal Order ◽

Recurrent Function ◽

Prony Method ◽

Interpolation Technique ◽

Linear Recurrent Sequence ◽

Grid Based

AbstractAn interpolation scheme on an equispaced grid based on the concept of the minimal order of the linear recurrent sequence is proposed in this paper. This interpolation scheme is exact when the number of nodes corresponds to the order of the linear recurrent function. It is shown that it is still possible to construct a nearest mimicking algebraic interpolant if the order of the linear recurrent function does not exist. The proposed interpolation technique can be considered as the extension of the Prony method and can be useful for describing noisy and defected signals.

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