Jacobi's iterative method for solving linear equations and the simulation of linear CNN

Abstract

It is shown that the application of Jacobi iteration to the linear algebraic equations obtained from the state equations of a linear CNN with constant input by setting the derivatives of the states to zero yields the steady-state solution of the state equations. It is proved that the Jacobi iteration equation and that obtained by setting the integration time-step a(00)(-1) in the discrete-time state equations obtained by the use of to Euler forward difference are the same. It is also shown that the exact pixel values of the output image can be calculated.