Infinitely many Zhang functions resulting in various ZNN models for time-varying matrix inversion with link to Drazin inverse. (English) Zbl 1342.65250
Summary: In this Letter, by generalizing the notion of Zhang functions (ZFs) from previous work, a novel general-form Zhang function (NGFZF) is proposed, developed and investigated. Specifically, based on the NGFZF, infinitely many ZFs (as error functions) can be readily generated by successively selecting the different values of its parameters. Besides, by employing the NGFZF, a novel general-form Zhang neural net (NGFZNN) is proposed and studied for real-time solution of a time-varying matrix inverse (also termed, Zhang matrix inverse, ZMI). Moreover, a link between ZMI and Drazin inverse is discovered and further generalized to solve for the time-varying Drazin inverse (TVDI).
MSC:
| 65Y05 | Parallel numerical computation |
| 15A09 | Theory of matrix inversion and generalized inverses |
| 65F30 | Other matrix algorithms (MSC2010) |
| 65Y10 | Numerical algorithms for specific classes of architectures |
Keywords:
parallel algorithms; real-time systems; Zhang neural net (ZNN); error functions; Zhang matrix inverse (ZMI); time-varying Drazin inverse (TVDI)References:
| [1] | Yi, C.; Chen, Y.; Lu, Z., Improved gradient-based neural networks for online solution of Lyapunov matrix equation, Inf. Process. Lett., 111, 16, 780-786 (2011) · Zbl 1260.68353 |
| [2] | Chen, K., Robustness analysis of Wang neural network for online linear equation solving, Electron. Lett., 48, 22, 1391-1392 (2012) |
| [3] | Chen, Y.; Yi, C.; Qiao, D., Improved neural solution for the Lyapunov matrix equation based on gradient search, Inf. Process. Lett., 113, 22-24, 876-881 (2013) · Zbl 1284.68492 |
| [4] | Zhang, Y.; Yi, C., Zhang Neural Networks and Neural-Dynamic Method (2011), Nova Science Publishers: Nova Science Publishers New York, USA |
| [5] | Zhang, Y.; Li, Z.; Guo, D.; Li, W.; Chen, P., Z-type and G-type models for time-varying inverse square root (TVISR) solving, Soft Comput., 17, 11, 2021-2032 (2013) |
| [6] | Zhang, Y.; Li, F.; Yang, Y.; Li, Z., Different Zhang functions leading to different Zhang-dynamics models illustrated via time-varying reciprocal solving, Appl. Math. Model., 36, 9, 4502-4511 (2012) · Zbl 1252.65222 |
| [7] | Guo, D.; Qiu, B.; Ke, Z.; Yang, Z.; Zhang, Y., Case study of Zhang matrix inverse for different ZFs leading to different nets, (Proc. of the IEEE World Congress on Computational Intelligence (2014)), 2764-2769 |
| [8] | Marcos, M. G.; Machado, J. A.T.; Azevedo-Perdicoúlis, T. P., A multi-objective approach for the motion planning of redundant manipulators, Appl. Soft Comput., 12, 2, 589-599 (2012) |
| [9] | Meyer, C. D.; Rose, N. J., The index and the Drazin inverse of block triangular matrices, SIAM J. Appl. Math., 33, 1, 1-7 (1977) · Zbl 0355.15009 |
| [10] | Zhong, J.; Liu, X.; Zhou, G.; Yu, Y., A new iterative method for computing the Drazin inverse, Filomat, 26, 3, 597-606 (2012) · Zbl 1289.65095 |
| [11] | Miljković, S.; Miladinović, M.; Stanimirović, P. S.; Wei, Y., Gradient methods for computing the Drazin-inverse solution, J. Comput. Appl. Math., 253, 255-263 (2013) · Zbl 1288.65033 |
| [12] | Zhang, Y.; Ke, Z.; Xu, P.; Yi, C., Time-varying square roots finding via Zhang dynamics versus gradient dynamics and the former’s link and new explanation to Newton-Raphson iteration, Inf. Process. Lett., 110, 24, 1103-1109 (2010) · Zbl 1380.65086 |
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