Finding all solutions of piecewise-linear resistive circuits with high approximation accuracy

An efficient algorithm is proposed for finding all solutions of piecewise-linear (PWL) resistive circuits with high approximation accuracy, namely, circuits where the characteristics of PWL resistors axe approximated by PWL functions with a very large number of segments. This algorithm is based on the LP test using the dual simplex method, the contraction method, and a special technique that makes the algorithm not require large memory space and not require copying tableaus. By numerical examples, it is shown that the proposed algorithm could find all solutions of a circuit where the number of PWL resistors is 4000 and the number of linear regions is 10000(4000).