Distance Fibonacci Polynomials by Graph Methods

Strzałka, Dominik; Wołski, S.; Włoch, Andrzej

doi:10.3390/sym13112075

Cited by 2 publications

(3 citation statements)

References 22 publications

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“…and the number of iterations n , the Fibonacci algorithm models of the k checkpoints iteration can be expressed as [6] :…”

Section: Principlesmentioning

confidence: 99%

Demodulation algorithm based on Fibonacci and cross-correlation for Fabry-Perot sensor

Lu,

Zeng,

Yang

et al. 2024

Third International Conference on Electronic Information Engineering and Data Processing (EIEDP 2024)

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Sensor technology plays an important role in the field of measurement science and engineering. Fabry-Perot (F-P) sensor has always been the focus of research due to its high precision and sensitivity. Traditional F-P sensor demodulation algorithms have limitations in terms of demodulation time and precision. In order to pursue higher accuracy and achieve faster demodulation, we report a joint demodulation algorithm based on Fibonacci and cross-correlation. The Fibonacci search method is used to quickly search the cavity length corresponding to the maximum cross-correlation number, and the target accuracy is achieved through search iteration. Experimental results show that this algorithm is used for Dual-Cavity Fabry-Perot Interferometer (DFPI) sensor demodulation, with a resolution of 10 pm and a cavity length demodulation time of less than 0.06 s. This study provides new insights for improving the demodulation efficiency and accuracy of F-P sensors.

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“…and the number of iterations n , the Fibonacci algorithm models of the k checkpoints iteration can be expressed as [6] :…”

Section: Principlesmentioning

confidence: 99%

Demodulation algorithm based on Fibonacci and cross-correlation for Fabry-Perot sensor

Lu,

Zeng,

Yang

et al. 2024

Third International Conference on Electronic Information Engineering and Data Processing (EIEDP 2024)

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“…• Approximate the highest time derivative function in (29) by Fibonacci wavelets. • Establish the system of algebraic equations (38).…”

Section: Algorithm 1 Algorithm For the Proposed Fibonacci Wavelet Met...mentioning

confidence: 99%

“…Subsequently, Catarino [28] defined a quaternion analogue of the h-Fibonacci polynomials of the form Q h,m (η) = ∑ 3 l=0 F h,m+l (η)e l , where F h,m (η) is the h(η)-Fibonacci polynomial. Recently, Strzałka et al [29] introduced a new class of Fibonacci polynomials coined as distance Fibonacci polynomials, which embodies the classical Fibonacci, Jacobsthal, and Narayana polynomials simultaneously. Owing to the nice characteristics of the Fibonacci polynomials, they have been extensively employed for solving differential equations [30], integro-differential equations [31], fractional delay differential equations [32], fractional differential equations [33], and many more.…”

Section: Introductionmentioning

confidence: 99%

Fibonacci Wavelet Method for the Solution of the Non-Linear Hunter–Saxton Equation

2022

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In this article, a novel and efficient collocation method based on Fibonacci wavelets is proposed for the numerical solution of the non-linear Hunter–Saxton equation. Firstly, the operational matrices of integration associated with the Fibonacci wavelets are constructed by following the strategy of Chen and Hsiao. The operational matrices merged with the collocation method are used to convert the given problem into a system of algebraic equations that can be solved by any classical method, such as Newton’s method. Moreover, the non-linearity arising in the Hunter–Saxton equation is handled by invoking the quasi-linearization technique. To show the efficiency and accuracy of the Fibonacci-wavelet-based numerical technique, the approximate solutions of the non-linear Hunter–Saxton equation with other numerical methods including the Haar wavelet, trigonometric B-spline, and Laguerre wavelet methods are compared. The numerical outcomes demonstrate that the proposed method yields a much more stable solution and a better approximation than the existing ones.

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Distance Fibonacci Polynomials by Graph Methods

Cited by 2 publications

References 22 publications

Demodulation algorithm based on Fibonacci and cross-correlation for Fabry-Perot sensor

Demodulation algorithm based on Fibonacci and cross-correlation for Fabry-Perot sensor

Fibonacci Wavelet Method for the Solution of the Non-Linear Hunter–Saxton Equation

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