Solving simultaneous linear equations using recurrent neural networks

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.