Realization of conjugate gradient algorithm on optical linear algebra processors.

Hybrid optoelectronic processors capable of manipulating matrices and vectors are known as optical linear algebra processors (OLAPs). Parallel implementations of several algorithms of computational linear algebra (such as Gaussian elimination, QR decomposition, and Richardson and Jacobi iterations) on OLAPs have been described in the last few years. A multiprocessor of ring structure is simply a network of parallel vector and scalar processors (optical or electronic) in which data are pipelined from a global memory and controller. A typical ring network is shown in Fig. 1. In this paper, we describe a parallel pipelined realization of the preconditioned conjugate gradient (PCCG) algorithm on a ring of OLAPs. The reasons for considering a parallel optical realization of the PCCG algorithm are: (1) PCCG is a popular algorithm in computational linear algebra and is used extensively in the solution of large systems of linear algebraic equations arising in the numerical solution of partial differential equations. (2) PCCG has uses in spectral estimation and may be helpful in adaptive signal processing.