This paper addresses some of the issues concerning the use of variable accuracy optical processors to improve the processing time required to obtain a high accuracy solution to a set of Linear Algebraic Equations (LAEs). We begin with a standard error analysis of the Steepest Descent iterative algorithm used to find the solution to the LAEs. This results in an expression relating the accuracy of the solution to the number of iterations and the inherent system accuracy in each mode of operation, along with the eigen-structure of the matrix describing the LAE. The accuracy at any iteration is a combination of terms representing the ideal algorithmic improvement plus the degradation due to processor inaccuracies. An evaluation of the proper number of iterations for processing in both low and high accuracy modes can be inferred through an examination of the tradeoffs in accuracy between these two terms. The expression is evaluated for several sample problems obtained from the Adaptive Phased Array Radar field. These results are then interpreted with respect to specific optical processing architectures.

Date Published: 11 August 1987
PDF: 8 pages
Proc. SPIE 0752, Digital Optical Computing, (11 August 1987); doi: 10.1117/12.939925

Published in SPIE Proceedings Vol. 0752:
Digital Optical Computing
Raymond Arrathoon, Editor(s)