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A polynomial array method is developed to extend array (table) techniques for polynomials with literal coefficients. Systematic procedures are presented for computing the coefficients of the polynomial in each array entry. The method is then applied for one- and two-dimensional discrete system stability tests. For one-dimensional systems, stability conditions for the system lead to a direct method for computing the critical gain. For two-dimensional filter stability tests, the proposed method removes the requirement for conjugate polynomials (or their coefficients) in constructing the array for a two-dimensional polynomials F(z1,z2) on mod z1 mod =1. It needs only simple computations on a set of second-order determinants with numerical entries and is very easy to program regardless of the orders of F(z1,z2).