Solving simultaneous linear equations using recurrent neural networks

doi:10.1016/0020-0255(94)90012-4

Information Sciences

Volume 76, Issues 3–4, 1994, Pages 255-277

https://doi.org/10.1016/0020-0255(94)90012-4 Get rights and content

Abstract

Simultaneous linear algebraic equations can be found in many mathematical model formulations. In monitoring and control of dynamic systems, there is often a need for solving simultaneous linear algebraic equations in real time. In this paper, recurrent neural networks for solving simultaneous linear algebraic equations are proposed. The asymptotic stability of the proposed neural networks and solvability of simultaneous linear equations by using the neural networks are substantiated. A circuit schematic for realizing the neural networks is described. The results of numerical simulations are discussed via illustrative examples. An extension of the recurrent neural networks for solving quadratic programming problems subject to equality constraints is also discussed.

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Citation Excerpt :
Many gradient-related methods have been announced in the scientific literature for finding the solutions of algebraic equations and computing the matrix inverse before the proposal of ZNN approach [8,32,33,35–37,52].
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View full text

Solving simultaneous linear equations using recurrent neural networks

Abstract

Comput. Operat. Res.

IEEE Trans. Neural Networks

Computing motion using analog and binary resistive networks

IEEE Trans. Comput.

Two-stage strategy for motion parameter estimation in dynamic images

Appl. Artificial Intelligence

Solving two-point boundary value problems in trajectory formation

Neural computation of decisions in optimization problems

Biol. Cybernet.

Simple neural optimization networks: an A/D converter, signal decision circuit, and a linear programming circuit

IEEE Trans. Circuits and Systems

Neural networks for nonlinear programming

IEEE Trans. Circuits and Systems

Optimization using neural networks

IEEE Trans. Comput.

On the asymptotic properties of recurrent neural networks for optimization

Int. J. Pattern Recognition and Artificial Intelligence