Matrix analysis
Analog VLSI and neural systems
Analog VLSI and neural systems
Recurrent Neural Networks for Computing Pseudoinverses of Rank-Deficient Matrices
SIAM Journal on Scientific Computing
Tikhonov Regularization and Total Least Squares
SIAM Journal on Matrix Analysis and Applications
Finite-Time Stability of Continuous Autonomous Systems
SIAM Journal on Control and Optimization
Springer Handbook of Robotics
From Zhang neural network to Newton iteration for matrix inversion
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Iterative method for computing the Moore-Penrose inverse based on Penrose equations
Journal of Computational and Applied Mathematics
A subspace approach to blind space-time signal processing forwireless communication systems
IEEE Transactions on Signal Processing
Face recognition by applying wavelet subband representation and kernel associative memory
IEEE Transactions on Neural Networks
Design and analysis of a general recurrent neural network model for time-varying matrix inversion
IEEE Transactions on Neural Networks
ISNN'13 Proceedings of the 10th international conference on Advances in Neural Networks - Volume Part II
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In this paper, a special class of recurrent neural network, termed Zhang neural network (ZNN), is investigated for the online solution of the time-varying matrix pseudoinverse. Meanwhile, a novel activation function, named Li activation function, is employed. Then, based on two basic Zhang functions (ZFs) and the intrinsically nonlinear method of ZNN design, two finite-time convergent ZNN models (termed ZNN-1 model and ZNN-2 model) are first proposed and investigated for time-varying matrix pseudoinversion. Such two ZNN models can be accelerated to finite-time convergence to the time-varying theoretical pseudoinverse. The upper bound of the convergence time is also derived analytically via Lyapunov theory. By exploiting the other three simplified ZFs and the extended nonlinearization method, three simplified finite-time convergent ZNN models (termed ZNN-3 model, ZNN-4 model and ZNN-5 model) are sequentially proposed. In addition, the link between the ZNN models and the Getz-Marsden (G-M) dynamic system is discovered and presented in this paper. Computer-simulation results further substantiate the theoretical analysis and demonstrate the effectiveness of ZNN models based on different ZFs for the time-varying matrix pseudoinverse.