Hybrid optical processor for systems of nonlinear equations

Abstract

A hybrid optical processor to solve a system of nonlinear equations is presented. The proposed system has been based on the Bimodal Optical Computer (BOC). Two algorithms based on the BOC are presented and compared. One algorithm solves the resulting system of linear equations approximately and the second solves the system exactly within a specified accuracy. The first is shown to result in a smaller number of iterations. The effect of errors from the I/O devices on the system is analyzed. Three factors affecting the convergence speed are considered: the initial values of the solution, the norm of the solution residue and the scale factor. It is shown that the number of iterations can be minimized when the norm of the residue is as small as possible, and the scale factor is equal to the ratio of the norm of the coefficient matrix to the norm of the residue. This processor has a speed advantage over digital processors for large size systems of equations.