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Realization Of Lanczos And Conjugate Gradient Algorithms On Optical Linear Algebra Processors

The Lanczos and conjugate gradient algorithms are important in computational linear algebra. In this paper, a parallel pipelined realization of these algorithms on a ring of optical linear algebra processors has been described. The flow of data is designed to minimize the idle times of the optical multiprocessor and the redundancy of computations. It is shown that optical pre conditioning can improve the accuracy of these algorithms substantially. Algorithms for optical preconditioning and results of numerical experiments are discussed. Since the Lanczos algorithm is used mostly with sparse matrices, a folded storage scheme to represent sparse matrices on spatial light modulators is discussed.