Complex recurrent neural network for computing the inverse and pseudo-inverse of the complex matrix
Applied Mathematics and Computation
Computers & Mathematics with Applications
International Journal of Knowledge-based and Intelligent Engineering Systems
Computers & Mathematics with Applications
A concise functional neural network for computing the extremum eigenpairs of real symmetric matrices
ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
A novel neural network approach for computing eigen-pairs of real antisymmetric matrices
AICI'12 Proceedings of the 4th international conference on Artificial Intelligence and Computational Intelligence
Improved neural solution for the Lyapunov matrix equation based on gradient search
Information Processing Letters
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Efficient computation of the largest modulus eigenvalues of a real anti-symmetric matrix is a very important problem in engineering. Using a neural network to complete these operations is in an asynchronous manner and can achieve high performance. This paper proposes a functional neural network (FNN) that can be transformed into a complex differential equation to do this work. Firstly, the mathematical analytic solution of the equation is received, and then the convergence properties of this FNN are analyzed. The simulation result indicates that with general initial complex values, the network will converge to the complex eigenvector corresponding to the eigenvalue whose imaginary part is positive, and modulus is the largest of all eigenvalues. Comparing with other neural networks used for computing eigenvalues and eigenvectors, this network is adaptive to real anti-symmetric matrices for completing these operations.