Abstract
Recently, a new computational test has been proposed for nonexistence of a solution to a system of nonlinear equations using linear programming. This test is termed the LP test. It has been shown that the LP test is much more powerful than the conventional nonexistence test if the system of nonlinear equations consists of many linear terms and a relatively small number of nonlinear terms. By introducing the LP test to interval analysis, all solutions of nonlinear equations can be found very efficiently. In this paper, we propose some techniques for improving the computational efficiency of the LP test in some special cases. Using the proposed techniques, all solutions of a special class of nonlinear equations (including circuit equations) can be found very efficiently.
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