Properties of a k-Order Linear Recursive Sequence Modulo m

1996 ◽  
pp. 505-519
Author(s):  
Marcellus E. Waddill
Keyword(s):  
Order Linear ◽  
Recursive Sequence

scholarly journals On the Sum of Reciprocal of Polynomial Applied to Higher Order Recurrences

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 638
Author(s):  
Pavel Trojovský
Keyword(s):  
Higher Order ◽  
Order Linear ◽  
Recursive Sequence ◽  
Infinite Sums ◽  
Reciprocal Sums

Recently a lot of papers have been devoted to partial infinite reciprocal sums of a higher-order linear recursive sequence. In this paper, we continue this program by finding a sequence which is asymptotically equivalent to partial infinite sums, including a reciprocal of polynomial applied to linear higher order recurrences.

scholarly journals Some New Identities of Second Order Linear Recurrence Sequences

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1496 ◽  
Author(s):  
Yanyan Liu ◽  
Xingxing Lv
Keyword(s):  
Power Series ◽  
Second Order ◽  
Linear Recurrence ◽  
Combinatorial Method ◽  
Order Linear ◽  
Computational Problem ◽  
Characteristic Roots ◽  
Recursive Sequence ◽  
Recurrence Sequences

The main purpose of this paper is using the combinatorial method, the properties of the power series and characteristic roots to study the computational problem of the symmetric sums of a certain second-order linear recurrence sequences, and obtain some new and interesting identities. These results not only improve on some of the existing results, but are also simpler and more beautiful. Of course, these identities profoundly reveal the regularity of the second-order linear recursive sequence, which can greatly facilitate the calculation of the symmetric sums of the sequences in practice.

scholarly journals On the Higher Power Sums of Reciprocal Higher-Order Sequences

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Zhengang Wu ◽  
Jin Zhang
Keyword(s):  
Error Estimation ◽  
Higher Order ◽  
Analytic Method ◽  
Order Linear ◽  
Power Sums ◽  
Higher Power ◽  
Recursive Sequence ◽  
Finite Sums ◽  
Reciprocal Sums

Let{un}be a higher-order linear recursive sequence. In this paper, we use the properties of error estimation and the analytic method to study the reciprocal sums of higher power of higher-order sequences. Then we establish several new and interesting identities relating to the infinite and finite sums.

CONTINUOUS-TIME FRACTIONAL ORDER LINEAR SYSTEMS IDENTIFICATION USING CHEBYSHEV WAVELET

2020 ◽  
Vol 6 (8(77)) ◽  
pp. 23-28
Author(s):  
Shuen Wang ◽  
Ying Wang ◽  
Yinggan Tang
Keyword(s):  
Linear Systems ◽  
Fractional Order ◽  
Continuous Time ◽  
Fractional Integration ◽  
Operational Matrices ◽  
Computation Complexity ◽  
Order Linear ◽  
Fractional Integration Operator ◽  
Systems Identification ◽  
Chebyshev Wavelet

In this paper, the identification of continuous-time fractional order linear systems (FOLS) is investigated. In order to identify the differentiation or- ders as well as parameters and reduce the computation complexity, a novel identification method based on Chebyshev wavelet is proposed. Firstly, the Chebyshev wavelet operational matrices for fractional integration operator is derived. Then, the FOLS is converted to an algebraic equation by using the the Chebyshev wavelet operational matrices. Finally, the parameters and differentiation orders are estimated by minimizing the error between the output of real system and that of identified systems. Experimental results show the effectiveness of the proposed method.

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