Abstract

We propose an iterative parallel solution algorithm for solving linear algebraic equations that is suitable for optical processing. This method is based on stationary-point search in particle motion and is applicable to any linear algebraic equation. By using central differences, we formulate the stationary-point-search algorithm in an iterative parallel form including the two parameters of artificial viscosity and time step, and the optimum values of these parameters are derived from a characteristic equation. Even though an ill-conditioned positive definite matrix is used instead of the original matrix in order to make the algorithm applicable to any matrix, the convergence property of this algorithm depends on the condition number of the original matrix. Computer simulations show that this method can be optimized by varying the parameters adaptively at every iteration, and we derive an adaptive stationary-point-search algorithm.

© 1989 Optical Society of America

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