Finding all solutions of piecewise-linear resistive circuits using linear programming

An efficient algorithm is proposed for finding all solutions of piecewise-linear resistive circuits. This algorithm is based on a new test for nonexistence of a solution to a system of piecewise-linear equations f_i(x)=0(i=1.2,···,n) in a super-region. Unlike the conventional sign test, which checks whether the solution surfaces of the single piecewise-linear equations exist or not in a super-region, the new test checks whether they intersect or not in the super-region. Such a test can be performed by using linear programming. It is shown that the simplex method can be performed very efficiently by exploiting the adjacency of super-regions in each step. The proposed algorithm is much more efficient than the conventional sign test algorithms and can find all solutions of large scale circuits very efficiently. Moreover, it can find all characteristic curves of piecewise-linear resistive circuits