Novel Complex-Valued Neural Network for Dynamic Complex-Valued Matrix Inversion

Bolin Liao; Lin Xiao; Jie Jin; Lei Ding; Mei Liu

doi:10.20965/jaciii.2016.p0132

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JACIII Vol.20 No.1 pp. 132-138

doi: 10.20965/jaciii.2016.p0132

(2016)

Paper:

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Novel Complex-Valued Neural Network for Dynamic Complex-Valued Matrix Inversion

Bolin Liao^, Lin Xiao^, Jie Jin^, Lei Ding^, and Mei Liu^**

^*College of Information Science and Engineering, Jishou University
Jishou 416000, China

^**College of Physics, Mechanical and Electrical Engineering, Jishou University
Jishou 416000, China

Received:

November 10, 2015

Accepted:

December 10, 2015

Online released:

January 19, 2016

Published:

January 20, 2016

Keywords:

complex-valued matrix inverse, gradient neural network, Zhang neural network, dynamic

Abstract

Static matrix inverse solving has been studied for many years. In this paper, we aim at solving a dynamic complex-valued matrix inverse. Specifically, based on the artful combination of a conventional gradient neural network and the recently-proposed Zhang neural network, a novel complex-valued neural network model is presented and investigated for computing the dynamic complex-valued matrix inverse in real time. A hardware implementation structure is also offered. Moreover, both theoretical analysis and simulation results substantiate the effectiveness and advantages of the proposed recurrent neural network model for dynamic complex-valued matrix inversion.

Cite this article as:

B. Liao, L. Xiao, J. Jin, L. Ding, and M. Liu, “Novel Complex-Valued Neural Network for Dynamic Complex-Valued Matrix Inversion,” J. Adv. Comput. Intell. Intell. Inform., Vol.20 No.1, pp. 132-138, 2016.

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References

[1] A. Benchabane, A. Bennia, F. Charif, and A. Taleb-Ahmed, “Multi-dimensional Capon spectral estimation using discrete Zhang neural networks,” Multidimensional Systems and Signal Processing, Vol.24, No.3, pp. 583-598, 2013.
[2] S. S. Ge, T. H. Lee, and C. J. Harris, “Adaptive Neural Network Control of Robotic Manipulators,” World Scientific, London, UK, 1998.
[3] D. Jwo and C. Lai, “Neural network-based GPS GDOP approximation and classification,” GPS Solutions, Vol.11, No.1, pp. 51-60, 2007.
[4] T. Sarkar, K. Siarkiewicz, and R. Stratton, “Survey of numerical methods for solution of large systems of linear equations for electromagnetic field problems,” IEEE Trans. on Antennas and Propagation, Vol.29, No.6, pp. 847-856, 1981.
[5] Y. Zhang, K. Chen, and H.-Z. Tan, “Performance analysis of gradient neural network exploited for online dynamic matrix inversion,” IEEE Trans. on Automatic Control, Vol.54, No.8, pp. 1940-1945, 2009.
[6] J. Wang, “A recurrent neural network for real-time matrix inversion,” Applied Mathematics and Computation, Vol.55, No.1, pp. 89-100, 1993.
[7] J. Hu and J. Wang, “Global stability of complex-valued recurrent neural networks with time-delays,” IEEE Trans. on Neural Networks and Learning Systems, Vol.23, No.6, pp. 853-865, 2012.
[8] S. Li and Y. Li, “Nonlinearly activated neural network for solving time-varying complex sylvester equation,” IEEE Trans. on Cybernetics, Vol.44, No.8, pp. 1397-1407, 2014.
[9] Y. Zhang and S. S. Ge, “Design and analysis of a general recurrent neural network model for time-varying matrix inversion,” IEEE Trans. on Neural Networks, Vol.16, No.6, pp. 1477-1490, 2005.
[10] D. Guo and Y. Zhang, “Zhang neural network for online solution of time-varying linear matrix inequality aided with an equality conversion,” IEEE Trans. on Neural Networks and Learning Systems, Vol.25, No.2, pp. 370-382, 2014.
[11] J. Song and Y. Yam, “Complex recurrent neural network for computing the inverse and pseudo-inverse of the complex matrix,” Applied Mathematics and Computation, Vol.93, No.2-3, pp. 195-205, 1998.
[12] B. Liao and Y. Zhang, “Different complex ZFs leading to different complex ZNN models for time-varying complex generalized inverse matrices,” IEEE Trans. on Neural Networks and Learning Systems, Vol.25, No.9, pp. 1621-1631, 2014.
[13] J. Wang, “Recurrent neural networks for solving systems of complex-valued linear equations,” Electronics Letters, Vol.28, No.18, pp. 1751-1753, 1992.
[14] J. Weickert, B.M.H. Romeny, and M.A. Viergever, “Efficient and reliable schemes for nonlinear diffusion filtering,” IEEE Trans. on Image Processing, Vol.7, No.3, pp. 398-410, 1998.
[15] B. Liao and Y. Zhang, “From different ZFs to different ZNN models accelerated via Li activation functions to finite-time convergence for time-varying matrix pseudoinversion,” Neurocomputing, Vol.133, pp. 512-522, 2014.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] A. Benchabane, A. Bennia, F. Charif, and A. Taleb-Ahmed, “Multi-dimensional Capon spectral estimation using discrete Zhang neural networks,” Multidimensional Systems and Signal Processing, Vol.24, No.3, pp. 583-598, 2013.

[2] [2] S. S. Ge, T. H. Lee, and C. J. Harris, “Adaptive Neural Network Control of Robotic Manipulators,” World Scientific, London, UK, 1998.

[3] [3] D. Jwo and C. Lai, “Neural network-based GPS GDOP approximation and classification,” GPS Solutions, Vol.11, No.1, pp. 51-60, 2007.

[4] [4] T. Sarkar, K. Siarkiewicz, and R. Stratton, “Survey of numerical methods for solution of large systems of linear equations for electromagnetic field problems,” IEEE Trans. on Antennas and Propagation, Vol.29, No.6, pp. 847-856, 1981.

[5] [5] Y. Zhang, K. Chen, and H.-Z. Tan, “Performance analysis of gradient neural network exploited for online dynamic matrix inversion,” IEEE Trans. on Automatic Control, Vol.54, No.8, pp. 1940-1945, 2009.

[6] [6] J. Wang, “A recurrent neural network for real-time matrix inversion,” Applied Mathematics and Computation, Vol.55, No.1, pp. 89-100, 1993.

[7] [7] J. Hu and J. Wang, “Global stability of complex-valued recurrent neural networks with time-delays,” IEEE Trans. on Neural Networks and Learning Systems, Vol.23, No.6, pp. 853-865, 2012.

[8] [8] S. Li and Y. Li, “Nonlinearly activated neural network for solving time-varying complex sylvester equation,” IEEE Trans. on Cybernetics, Vol.44, No.8, pp. 1397-1407, 2014.

[9] [9] Y. Zhang and S. S. Ge, “Design and analysis of a general recurrent neural network model for time-varying matrix inversion,” IEEE Trans. on Neural Networks, Vol.16, No.6, pp. 1477-1490, 2005.

[10] [10] D. Guo and Y. Zhang, “Zhang neural network for online solution of time-varying linear matrix inequality aided with an equality conversion,” IEEE Trans. on Neural Networks and Learning Systems, Vol.25, No.2, pp. 370-382, 2014.

[11] [11] J. Song and Y. Yam, “Complex recurrent neural network for computing the inverse and pseudo-inverse of the complex matrix,” Applied Mathematics and Computation, Vol.93, No.2-3, pp. 195-205, 1998.

[12] [12] B. Liao and Y. Zhang, “Different complex ZFs leading to different complex ZNN models for time-varying complex generalized inverse matrices,” IEEE Trans. on Neural Networks and Learning Systems, Vol.25, No.9, pp. 1621-1631, 2014.

[13] [13] J. Wang, “Recurrent neural networks for solving systems of complex-valued linear equations,” Electronics Letters, Vol.28, No.18, pp. 1751-1753, 1992.

[14] [14] J. Weickert, B.M.H. Romeny, and M.A. Viergever, “Efficient and reliable schemes for nonlinear diffusion filtering,” IEEE Trans. on Image Processing, Vol.7, No.3, pp. 398-410, 1998.

[15] [15] B. Liao and Y. Zhang, “From different ZFs to different ZNN models accelerated via Li activation functions to finite-time convergence for time-varying matrix pseudoinversion,” Neurocomputing, Vol.133, pp. 512-522, 2014.

Novel Complex-Valued Neural Network for Dynamic Complex-Valued Matrix Inversion

Bolin Liao*, Lin Xiao*, Jie Jin*, Lei Ding*, and Mei Liu**

Bolin Liao^, Lin Xiao^, Jie Jin^, Lei Ding^, and Mei Liu^**