A finite-time convergent Zhang neural network and its application to real-time matrix square root finding
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In this paper, a finite-time convergent Zhang neural network (ZNN) is proposed and studied for matrix square root finding. Compared to the original ZNN (OZNN) model, the finite-time convergent ZNN (FTCZNN) model fully utilizes a nonlinearly activated sign-bi-power function, and thus possesses faster convergence ability. In addition, the upper bound of convergence time for the FTCZNN model is theoretically derived and estimated by solving differential inequalities. Simulative comparisons are further conducted between the OZNN model and the FTCZNN model under the same conditions. The results validate the effectiveness and superiority of the FTCZNN model for matrix square root finding.
KeywordsZhang neural networks Matrix square root Finite-time convergence Nonlinear activation function Upper bound
This work is supported by the Natural Science Foundation of Hunan Province, China (grant no. 2016JJ2101), the National Natural Science Foundation of China (grant no. 61503152), the Research Foundation of Education Bureau of Hunan Province, China (grant no. 15B192), the National Natural Science Foundation of China (grant nos. 61563017, 61561022, 61363073, and 61363033), and the Research Foundation of Jishou University, China (grant nos. 2015SYJG034, JGY201643, and JG201615). In addition, the author thanks the editors and anonymous reviewers for their valuable suggestions and constructive comments which have really helped the author improve the presentation and quality of this paper very much.
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Conflict of interests
The author declares that he has no conflict of interest.
- 3.Meini B (2003) The matrix square root from a new functional perspective: theoretical results and computational issues Technical Report, vol 1455. Dipartimento di Matematica, Università di Pisa, PisaGoogle Scholar
- 4.Long J, Hu X, Zhang L (2008) Newton’s method with exact line search for the square root of a matrix. J Phys Conf Ser 96:1–5Google Scholar
- 6.Mohammed AH, Ali AH, Syed R (2000) Fixed point iterations for computing square roots and the matrix sign function of complex matrices Proceedings IEEE international conference on decision and control, pp 4253–4258Google Scholar
- 15.Zhang Y (2005) Revisit the analog computer and gradient-based neural system for matrix inversion Proceedings IEEE international symposium on intelligent control, pp 1411–1416Google Scholar
- 21.Xiao L, Zhang Y (2014) From different Zhang functions to various ZNN models accelerated to finite-time convergence for time-varying linear matrix equation. Inform Process Lett 39(3): 309–326Google Scholar
- 22.Jin L, Zhang Y, Qiu B (2016) Neural network-based discrete-time Z-type model of high accuracy in noisy environments for solving dynamic system of linear equations. Neural Comput. App., Accepted, doi: 10.1007/s00521-016-2640-x