LU and Cholesky decomposition on an optical systolic array processor

Abstract

Direct solutions of matrix-vector equations on an optical systolic array processor are considered. The solutions are discussed and a parallel algorithm for LU matrix decomposition that is very attractive for an optical realization is formulated. It is noted that when direct techniques are used, it is preferable to realize the matrix decomposition on an optical system and to utilize a digital processor for the solution of the simplified resultant matrix-vector problem. One method of realizing LU matrix decomposition on a new frequency-multiplexed optical systolic array matrix-matrix processor is described. A simple method for extending the process of LU decomposition to Cholesky decomposition on the optical processor is discussed.