Recurrent Neural Networks for Computing Pseudoinverses of Rank-Deficient Matrices

Authors:
Jun Wang
Affiliations:
-
Venue:
SIAM Journal on Scientific Computing
Year:
1997

Citing 0
Cited 11

A recurrent neural network computing the largest imaginary or real part of eigenvalues of real matrices

Computers & Mathematics with Applications
Intelligent computing for real-time solution of time-varying linear equations

International Journal of Intelligent Systems Technologies and Applications
Repetitive motion of redundant robots planned by three kinds of recurrent neural networks and illustrated with a four-link planar manipulator's straight-line example

Robotics and Autonomous Systems
The minimum-variance theory revisited

IWANN'03 Proceedings of the Artificial and natural neural networks 7th international conference on Computational methods in neural modeling - Volume 1
Bi-criteria velocity minimization of robot manipulators using lvi-based primal-dual neural network and illustrated via puma560 robot arm

Robotica
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
Brief Augmented gradient flows for on-line robust pole assignment via state and output feedback

Automatica (Journal of IFAC)
Recurrent neural networks for nonlinear output regulation

Automatica (Journal of IFAC)
Different Zhang functions leading to different ZNN models illustrated via time-varying matrix square roots finding

Expert Systems with Applications: An International Journal
A novel iterative method for computing generalized inverse

Neural Computation
From different ZFs to different ZNN models accelerated via Li activation functions to finite-time convergence for time-varying matrix pseudoinversion

Neurocomputing

Quantified Score

Hi-index	0.01

Visualization

Abstract

Three recurrent neural networks are presented for computing the pseudoinverses of rank-deficient matrices. The first recurrent neural network has the dynamical equation similar to the one proposed earlier for matrix inversion and is capable of Moore--Penrose inversion under the condition of zero initial states. The second recurrent neural network consists of an array of neurons corresponding to a pseudoinverse matrix with decaying self-connections and constant connections in each row or column. The third recurrent neural network consists of two layers of neuron arrays corresponding, respectively, to a pseudoinverse matrix and a Lagrangian matrix with constant connections. All three recurrent neural networks are also composed of a number of independent subnetworks corresponding to the rows or columns of a pseudoinverse. The proposed recurrent neural networks are shown to be capable of computing the pseudoinverses of rank-deficient matrices.