title: Direct and implicit optical matrix-vector algorithms.
abstract: New direct and implicit algorithms for optical matrix-vector and systolic array processors are considered. Direct rather than indirect algorithms to solve linear systems and implicit rather than explicit solutions to solve second-order partial differential equations are discussed. In many cases, such approaches more properly utilize the advantageous features of optical systolic array processors. The matrix-decomposition operation (rather than solution of the simplified matrix-vector equation that results) is recognized as the computationally burdensome aspect of such problems that should be computed on an optical system. The Householder QR matrix-decomposition algorithm is considered as a specific example of a direct solution. Extensions to eigenvalue computation and formation of matrices of special structure are also noted.
authors.affiliation: Carnegie-Mellon University, Department of Electrical Engineering, Pittsburgh, Pennsylvania 15213, USA.
authors.forename: D
authors.initials: D
authors.lastname: Casasent
authors.forename: A
authors.initials: A
authors.lastname: Ghosh