Numerical analysis of simultaneous nonlinear algebraic equations

J.B. Moore's (J. Assoc. Comp. Math., vol.14, p.311-5, 1976) method of solving a single-variable algebraic equation is generalized to a method for multivariable simultaneous algebraic equations. The proposed method makes use of an objective function similar to the Lyapunov function, but it has multiple-zero points corresponding to the solution of the original algebraic equation. Using the proposed method, all solutions of a simultaneous nonlinear algebraic equation with complex coefficients are obtained for both real and complex roots.<>