Iterative Solutions To Nonlinear Matrix Equations Using A Fixed Number Of Steps

D. Casasent; A. Ghosh; C. P. Neuman

doi:10.1117/12.944014

28 November 1984 Iterative Solutions To Nonlinear Matrix Equations Using A Fixed Number Of Steps

D. Casasent, A. Ghosh, C. P. Neuman

Proceedings Volume 0495, Real-Time Signal Processing VII; (1984) https://doi.org/10.1117/12.944014
Event: 28th Annual Technical Symposium, 1984, San Diego, United States

Abstract

An iterative algorithm for the solution of a quadratic matrix equation (the algebraic Ricatti equation) is detailed. This algorithm is unique in that it allows the solution of a nonlinear matrix equation in a finite number of iterations to a desired accuracy. Theoretical rules for selection of the operation parameters and number of iterations required are advanced and simulation verification and quantitative performance on an error-free processor are provided. An error source model for an optical linear algebra processor is then advanced, analyzed and simulated to verify and quantify our performance guidelines. A comparison of iterative and direct solutions of linear algebraic equations is then provided. Experimental demonstrations on a laboratory optical linear algebra processor are included for final confirmation. Our theoretical results, error source treatment and guidelines are appropriate for digital systolic processor implementation and for digital-optical processor analysis.

Citation Download Citation

D. Casasent, A. Ghosh, and C. P. Neuman "Iterative Solutions To Nonlinear Matrix Equations Using A Fixed Number Of Steps", Proc. SPIE 0495, Real-Time Signal Processing VII, (28 November 1984); https://doi.org/10.1117/12.944014

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