Recurrent neural network for solving linear matrix equation

Abstract

In this paper Recurrent neural networks for solving linear matrix equations are proposed. we give an overview of recent research into recurrent algorithms for the solution of linear matrix equations. The problem of solving matrix or vector equations is widely encountered in many different science and engineering fields, as it is usually an essential part in many solutions and applications. Recent research has been directed towards the online solution of algebraic equations, which especially includes matrix inversion and linear equation solving. A new recurrent neural network (RNN) is presented for solving online linear time-invariant (LTI) equations, which has been developed based ingeniously on a vector-valued error-function rather than a scalar-valued norm-based function. Theoretical analysis and simulation results both substantiate the efficacy of such an RNN model for online LTI equation solving.