New Formulas Involving Fibonacci and Certain Orthogonal Polynomials

Abd-Elhameed, W. M.; Ahmed, H. M.; Napoli, Anna; Kowalenko, Victor

doi:10.3390/sym15030736

Cited by 4 publications

(2 citation statements)

References 33 publications

(46 reference statements)

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“…In the context of regression, polynomials enable model flexibility as they can model non-linear relationships between variables [25]. The application of polynomial regression is particularly useful in situations where simple linear models do not provide sufficiently accurate predictions, making polynomial regression a powerful tool in data analysis and machine learning [26,27]. Qian et al (2018) [28] developed different regression models in their research for predicting the calorific value based on the inputs of proximal analysis.…”

Section: Introductionmentioning

confidence: 99%

Biomass Higher Heating Value Estimation: A Comparative Analysis of Machine Learning Models

Brandić,

Pezo,

Voća

et al. 2024

Energies

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The research conducted focused on the capabilities of various non-linear and machine learning (ML) models in estimating the higher heating value (HHV) of biomass using proximate analysis data as inputs. The research was carried out to identify the most appropriate model for the estimation of HHV, which was determined by a statistical analysis of the modeling error. In this sense, artificial neural networks (ANNs), support vector machine (SVM), random forest regression (RFR), and higher-degree polynomial models were compared. After statistical analysis of the modeling error, the ANN model was found to be the most suitable for estimating the HHV biomass and showed the highest specific regression coefficient, with an R2 of 0.92. SVM (R2 = 0.81), RFR, and polynomial models (R2 = 0.84), on the other hand, also exhibit a high degree of estimation, albeit with somewhat larger modelling errors. The study conducted suggests that ANN models are best suited for the non-linear modeling of HHV of biomass, as they can generalize and search for links between input and output data that are more robust but also more complex in structure.

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Section: Introductionmentioning

confidence: 99%

Biomass Higher Heating Value Estimation: A Comparative Analysis of Machine Learning Models

Brandić,

Pezo,

Voća

et al. 2024

Energies

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“…In the paper [1], novel formulas for Fibonacci polynomials are developed, encompassing higher-order derivatives and recurrent integrals, all expressed in relation to Fibonacci polynomials. These findings are subsequently employed to address connectivity issues bridging the gap between Fibonacci polynomials and orthogonal polynomials.…”

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confidence: 99%

Recent Advances in Special Functions and Their Applications

Choi

2023

Symmetry

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Novel Approach by Shifted Fibonacci Polynomials for Solving the Fractional Burgers Equation

Alharbi,

Abu Sunayh,

Atta

et al. 2024

Fractal Fract

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This paper analyzes a novel use of the shifted Fibonacci polynomials (SFPs) to treat the time-fractional Burgers equation (TFBE). We first develop the fundamental formulas of these polynomials, which include their power series representation and the inversion formula. We establish other new formulas for the SFPs, including integer and fractional derivatives, in order to design the collocation approach for treating the TFBE. These derivative formulas serve as tools that aid in constructing the operational metrics for the integer and fractional derivatives of the SFPs. We use these matrices to transform the problem and its underlying conditions into a system of nonlinear equations that can be treated numerically. An error analysis is analyzed in detail. We also present three illustrative numerical examples and comparisons to test our proposed algorithm. These results showed that the proposed algorithm is advantageous since highly accurate approximate solutions can be obtained by choosing a few terms of retained modes of SFPs.

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New Formulas Involving Fibonacci and Certain Orthogonal Polynomials

Cited by 4 publications

References 33 publications

Biomass Higher Heating Value Estimation: A Comparative Analysis of Machine Learning Models

Biomass Higher Heating Value Estimation: A Comparative Analysis of Machine Learning Models

Recent Advances in Special Functions and Their Applications

Novel Approach by Shifted Fibonacci Polynomials for Solving the Fractional Burgers Equation

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