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Search Results (2)

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Keywords = complex-valued quasi-interpolation operator

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11 pages, 230 KB  
Article
Symmetrized, Perturbed Hyperbolic Tangent-Based Complex-Valued Trigonometric and Hyperbolic Neural Network Accelerated Approximation
by George A. Anastassiou
Mathematics 2025, 13(10), 1688; https://doi.org/10.3390/math13101688 - 21 May 2025
Cited by 1 | Viewed by 865
Abstract
In this study, we research the univariate quantitative symmetrized approximation of complex-valued continuous functions on a compact interval by complex-valued symmetrized and perturbed neural network operators. These approximations are derived by establishing Jackson-type inequalities involving the modulus of continuity of the used function’s [...] Read more.
In this study, we research the univariate quantitative symmetrized approximation of complex-valued continuous functions on a compact interval by complex-valued symmetrized and perturbed neural network operators. These approximations are derived by establishing Jackson-type inequalities involving the modulus of continuity of the used function’s high order derivatives. The kinds of our approximations are trigonometric and hyperbolic. Our symmetrized operators are defined by using a density function generated by a q-deformed and λ-parametrized hyperbolic tangent function, which is a sigmoid function. These accelerated approximations are pointwise and of the uniform norm. The related complex-valued feed-forward neural networks have one hidden layer. Full article
16 pages, 530 KB  
Article
Cutting-Edge Computational Approaches for Approximating Nonlocal Variable-Order Operators
by Nayereh Tanha, Behrouz Parsa Moghaddam and Mousa Ilie
Computation 2024, 12(1), 14; https://doi.org/10.3390/computation12010014 - 12 Jan 2024
Cited by 1 | Viewed by 2286
Abstract
This study presents an algorithmically efficient approach to address the complexities associated with nonlocal variable-order operators characterized by diverse definitions. The proposed method employs integro spline quasi interpolation to approximate these operators, aiming for enhanced accuracy and computational efficiency. We conduct a thorough [...] Read more.
This study presents an algorithmically efficient approach to address the complexities associated with nonlocal variable-order operators characterized by diverse definitions. The proposed method employs integro spline quasi interpolation to approximate these operators, aiming for enhanced accuracy and computational efficiency. We conduct a thorough comparison of the outcomes obtained through this approach with other established techniques, including finite difference, IQS, and B-spline methods, documented in the applied mathematics literature for handling nonlocal variable-order derivatives and integrals. The numerical results, showcased in this paper, serve as a compelling validation of the notable advantages offered by our innovative approach. Furthermore, this study delves into the impact of selecting different variable-order values, contributing to a deeper understanding of the algorithm’s behavior across a spectrum of scenarios. In summary, this research seeks to provide a practical and effective solution to the challenges associated with nonlocal variable-order operators, contributing to the applied mathematics literature. Full article
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