An effective use for analog optical vector processors is in the implementation of robust computational algorithms that require a high throughput rate but exhibit tolerance for roundoff errors and noise. Matrix preconditioning algorithms used for preprocessing the data of linear algebraic equations have these properties. In this paper, the performance of polynomial matrix preconditioning algorithms realized on optical processors is analyzed. The results of the error analysis and simulations show that for a given set of data the spatial errors and detector noise below a certain threshold level do not affect the accuracy of the optical preconditioning. Formulas for calculating such thresholds of tolerable amounts of optical errors are derived. The effects of optical preconditioning on the final solution of a system of linear algebraic equations are also analyzed, and it is found that optical preconditioning improves the rate of convergence and the final accuracy. Thus simple and efficient optical preprocessors can be designed with preconditioning algorithms to assist parallel solvers of linear algebraic equations.
© 1988 Optical Society of AmericaFull Article | PDF Article
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