Matrix computations and equation solving using structured networks and training

Abstract

Three structured networks and their corresponding training algorithms are proposed for matrix QR factorization eigenvalue and eigenvector determination, and Lyapunov equation solving. The basic procedure behind these approaches is as follows: represent a given problem by a structured network, train this structured network to match some desired patterns, and obtain the solution to the problem from the weights of the resulting structured network. A general-purpose programmable network architecture is proposed which can be programmed to solve different problems. Simulation results showed that the proposed approaches worked quite well.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>