Finding All Solutions of Nonlinear Systems of Equations Using Linear Programming with Guaranteed Accuracy

A linear programming-based method is presented for nding all solutions of nonlinear systems of equations with guaranteed accuracy. In this method, a new e ective linear programming-based method is used to delete regions in which solutions do not exist. On the other hand, Krawczyk's method is used to nd regions in which solutions exist. As an illustrative example, all solutions of the nonlinear system of equations describing equilibrium conditions of the \high polymer liquid system", which is a well-known ill-conditioned system of equations, are identi ed by the method.