Time-Varying Pseudoinversion Based on Full-Rank Decomposition and Zeroing Neural Networks
Abstract
:1. Introduction
- A new ZNN model, called ZNNFRDP, for the calculation of the time-varying pseudoinverse based on FRD is introduced and investigated. Keep in mind that ZNNFRDP stands for ZNN model based on FRD for the calculation of pseudoinverse.
- Theoretical analysis supported by five numerical experiments show that the ZNNFRDP model performs as well as, if not better than, other well-performing ZNN models in the computation of the time-varying pseudoinverse.
2. Materials and Methods
Algorithm 1. Matrix Q calculation. |
Require: The number of columns n and rows r of matrix .
Ensure: The matrix Q. |
Algorithm 2. Matrix G calculation. |
Require: The number of columns n and rows r of matrix .
Ensure: The matrix G. |
Algorithm 3. Matrix R calculation. |
Require: A real symmetric matrix’s column or row number r.
Ensure: The matrix R. |
3. Results
3.1. Experiment 1
3.2. Experiment 2
3.3. Experiment 3
3.4. Experiment 4
3.5. Experiment 5
4. Discussion
- The convergence of the ZNNFRDP model starts from a non-optimal initial price and converge in a small period of time to the zero matrix.
- The errors caused in the Moore-Penrose equations (i)–(iv) and the and solutions trajectories act consistently due to the EMEGs’ proclivity toward convergence.
- The EMEGs will converge more quickly when the price of the design parameter is greater.
- The ZNNFRDP model performs as well as, if not better than, the ZNNP and ZNNSVDP models.
- In essence, the time-varying pseudoinverses are calculated with exceptional and efficient performance by the ZNNFRDP model.
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Alharbi, H.; Jerbi, H.; Kchaou, M.; Abbassi, R.; Simos, T.E.; Mourtas, S.D.; Katsikis, V.N. Time-Varying Pseudoinversion Based on Full-Rank Decomposition and Zeroing Neural Networks. Mathematics 2023, 11, 600. https://doi.org/10.3390/math11030600
Alharbi H, Jerbi H, Kchaou M, Abbassi R, Simos TE, Mourtas SD, Katsikis VN. Time-Varying Pseudoinversion Based on Full-Rank Decomposition and Zeroing Neural Networks. Mathematics. 2023; 11(3):600. https://doi.org/10.3390/math11030600
Chicago/Turabian StyleAlharbi, Hadeel, Houssem Jerbi, Mourad Kchaou, Rabeh Abbassi, Theodore E. Simos, Spyridon D. Mourtas, and Vasilios N. Katsikis. 2023. "Time-Varying Pseudoinversion Based on Full-Rank Decomposition and Zeroing Neural Networks" Mathematics 11, no. 3: 600. https://doi.org/10.3390/math11030600
APA StyleAlharbi, H., Jerbi, H., Kchaou, M., Abbassi, R., Simos, T. E., Mourtas, S. D., & Katsikis, V. N. (2023). Time-Varying Pseudoinversion Based on Full-Rank Decomposition and Zeroing Neural Networks. Mathematics, 11(3), 600. https://doi.org/10.3390/math11030600