1 April 1989 High Speed Matrix Preprocessing On Analog Optical Associative Processors
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Abstract
The accuracy of matrix computations performed on analog optical associative processors is limited by noise and spatial wavefront errors. Earlier studies show that the rate of convergence and accuracy of analog optical matrix data processing can be improved by lowering the condition number of the data matrix. In this paper, we describe a new preprocessing technique, the split-step polynomial preconditioning algorithm, that can reduce the condition number of a matrix efficiently. With a few additional steps, this algorithm can be used to calculate the inverse or to estimate the condition number of a matrix. A realization of this preprocessing algorithm on optical associative processors is considered, and its performance and complexity are analyzed. The results of numerical experiments on case studies with ill-conditioned matrices show that this new preprocessing algorithm is a practicable tool for improving the perfor-mance of analog optical processors. Preliminary analyses of the new preconditioning algorithm demonstrate its robustness with regard to the spatial errors and random noise present in most analog optical computing systems.
Anjan Ghosh, Anjan Ghosh, Palacharla Paparao, Palacharla Paparao, } "High Speed Matrix Preprocessing On Analog Optical Associative Processors," Optical Engineering 28(4), 284354 (1 April 1989). https://doi.org/10.1117/12.7976962 . Submission:
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