Neural Networks for Optimization and Signal Processing
Neural Networks for Optimization and Signal Processing
A neural root finder of polynomials based on root moments
Neural Computation
A general methodology for designing globally convergent optimization neural networks
IEEE Transactions on Neural Networks
A constructive approach for finding arbitrary roots of polynomials by neural networks
IEEE Transactions on Neural Networks
Neurodynamic Analysis for the Schur Decomposition of the Box Problems
Computational Intelligence and Security
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This paper presents a novel recurrent time continuous neural network model for solving eigenvalue and eigenvector problem. The network is proved to be globally convergent to an exact eigenvector of a matrix A with respect to the problem's feasible region. This convergence is called quasi-convergence in the sense of the starting point to be in the feasible set. It also demonstrates that the network is primal in the sense that the network's neural trajectories will never escape from the feasible region when starting at it. By using an energy function, the network's stable point set is guaranteed to be the eigenvector set of the involved matrix. Compared with the existing neural network models for eigenvalue problem, the new model's performance is more effective and more reliable. Moreover, simulation results are given to illustrate further the global convergence and the fundamental validity of the proposed neural network for eigenvalue problem.