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.
© 1983 Optical Society of America
Original Manuscript: May 4, 1983
Published: November 15, 1983
David Casasent and Anjan Ghosh, "Direct and implicit optical matrix–vector algorithms," Appl. Opt. 22, 3572-3578 (1983)