Version 1
: Received: 8 August 2024 / Approved: 8 August 2024 / Online: 9 August 2024 (00:20:25 CEST)
How to cite:
Čajić, E.; Stojanović, Z.; Galić, D. Hybrid Approaches for Eigenvalues and Eigenvectors: Neural Networks and Traditional Methods. Preprints2024, 2024080625. https://doi.org/10.20944/preprints202408.0625.v1
Čajić, E.; Stojanović, Z.; Galić, D. Hybrid Approaches for Eigenvalues and Eigenvectors: Neural Networks and Traditional Methods. Preprints 2024, 2024080625. https://doi.org/10.20944/preprints202408.0625.v1
Čajić, E.; Stojanović, Z.; Galić, D. Hybrid Approaches for Eigenvalues and Eigenvectors: Neural Networks and Traditional Methods. Preprints2024, 2024080625. https://doi.org/10.20944/preprints202408.0625.v1
APA Style
Čajić, E., Stojanović, Z., & Galić, D. (2024). Hybrid Approaches for Eigenvalues and Eigenvectors: Neural Networks and Traditional Methods. Preprints. https://doi.org/10.20944/preprints202408.0625.v1
Chicago/Turabian Style
Čajić, E., Zvezdan Stojanović and Dario Galić. 2024 "Hybrid Approaches for Eigenvalues and Eigenvectors: Neural Networks and Traditional Methods" Preprints. https://doi.org/10.20944/preprints202408.0625.v1
Abstract
This paper explores innovative approaches to determining eigenvalues and eigenvectors through the combination of neural networks and traditional numerical methods. Traditional methods like the Newton-Raphson and Durand-Kerner algorithms are proven effective but often require good initial approximations and can be sensitive to the choice of starting points. In this study, we propose a hybrid approach that uses neural networks to generate better initial approximations, which are then iteratively refined using traditional methods. By combining the pattern recognition power of neural networks with the adaptability of traditional numerical methods, we demonstrate faster convergence and higher accuracy in determining eigenvalues and eigenvectors. Experimental results on various polynomials of different degrees and characteristics show that our hybrid approach outperforms individual methods, providing a more robust and efficient solution.
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
