Journal ArticleDOI
Neural network approach to computing matrix inversion
Luo Fa-Long,Bao Zheng +1 more
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TLDR
It is shown both analytically and by simulations that this network is guaranteed to be stable and to provide results arbitrarily close to the accurate inversion of a matrix within an elapsed time of only a few characteristic time constants of the network.About:
This article is published in Applied Mathematics and Computation.The article was published on 1992-02-01. It has received 57 citations till now. The article focuses on the topics: Interconnection & Artificial neural network.read more
Citations
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Journal ArticleDOI
Design and analysis of a general recurrent neural network model for time-varying matrix inversion
Yunong Zhang,Shuzhi Sam Ge +1 more
TL;DR: Simulation results substantiate the theoretical analysis and demonstrate the efficacy of the neural model on time-varying matrix inversion, especially when using a power-sigmoid activation function.
Journal ArticleDOI
A recurrent neural network for solving Sylvester equation with time-varying coefficients
TL;DR: The recurrent neural network with implicit dynamics is deliberately developed in the way that its trajectory is guaranteed to converge exponentially to the time-varying solution of a given Sylvester equation.
Journal ArticleDOI
A recurrent neural network for real-time matrix inversion
TL;DR: The proposed recurrent neural network is proven to be asymptotically stable and capable of computing large-scale nonsingular inverse matrices in real-time.
Journal ArticleDOI
Recurrent Neural Networks for Computing Pseudoinverses of Rank-Deficient Matrices
TL;DR: Three recurrent neural networks are presented for computing the pseudoinverses of rank-deficient matrices with dynamical equation similar to the one proposed earlier for matrix inversion and capable of Moore--Penrose inversion under the condition of zero initial states.
Proceedings ArticleDOI
Revisit the Analog Computer and Gradient-Based Neural System for Matrix Inversion
TL;DR: A general neural system for matrix inversion is presented which can be constructed by using monotonically-increasing odd activation functions, and an application example on inverse-kinematic control of redundant manipulators via online pseudoinverse solution is presented.
References
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Book
Adaptive Signal Processing
Bernard Widrow,Samuel D. Stearns +1 more
TL;DR: This chapter discusses Adaptive Arrays and Adaptive Beamforming, as well as other Adaptive Algorithms and Structures, and discusses the Z-Transform in Adaptive Signal Processing.
Journal ArticleDOI
Cellular neural networks: theory
Leon O. Chua,L. Yang +1 more
TL;DR: In this article, a class of information processing systems called cellular neural networks (CNNs) are proposed, which consist of a massive aggregate of regularly spaced circuit clones, called cells, which communicate with each other directly through their nearest neighbors.
Journal ArticleDOI
Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit
David W. Tank,John J. Hopfield +1 more
TL;DR: In this article, the analog-to-digital (A/D) conversion was considered as a simple optimization problem, and an A/D converter of novel architecture was designed.
Journal ArticleDOI
Neural networks for nonlinear programming
TL;DR: In this paper, the dynamics of the modified canonical nonlinear programming circuit are studied and how to guarantee the stability of the network's solution, by considering the total cocontent function.
Journal ArticleDOI
Frequency estimation by principal component AR spectral estimation method without eigendecomposition
Steven Kay,Arnab K. Shaw +1 more
TL;DR: An eigenvalue filtering method is proposed that applies a transformation to an autocorrelation matrix, which has the effect of truncating the undesired eigenvalues so that the corresponding matrix function closely approximates the pseudoinverse.