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Stable factorization of 2-D polynomials using neural networks

A method is presented for the factorization of 2D second order polynomials, based on the application of artificial neural networks trained by constrained learning techniques. The approach achieves minimization of the usual mean square error criterion along with simultaneous satisfaction of constraints between the polynomial coefficients. Using this method, we are able to obtain the exact solution for factorable polynomials and good approximate solutions for nonfactorable polynomials. By incorporating additional constraints for stability into the formalism our method can be successfully used for the realization of stable IIR filters in cascade form.