Find all solutions of piecewise-linear resistive circuits using an LP test

Finding all solutions of piecewise‐linear resistive circuits using the dual simplex method

“…The discussion of this paper is easily extended to the case where g(x) contains non-separable functions of more than one variable [16]. In this paper, we discuss the problem of ÿnding all solutions of (1) contained in an initial region D that is given by an n-dimensional rectangle.…”

“…We ÿrst review the LP test algorithm proposed in Reference [16], which is the basis of the proposed algorithm.…”

“…Hence, the size of the tableau is (3n + 1)×(2n + 1). The basic algorithm for ÿnding all solutions of Equation (1) using the LP test is as follows [16]. Beginning with the initial region D, the following procedure is performed recursively.…”

“…The idea of using LP for ÿnding all solutions of PWL-resistive circuits was proposed ÿrst in Reference [7] and extended in References [11,12,15,16]. This idea was further extended to ÿnding all solutions of general non-linear equations [17].…”

“…For this problem, many e cient algorithms have been proposed [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], but no algorithm has been used in practical circuit simulation. One of the di culties of this problem is that the number of linear regions to be analysed grows exponentially with the number of PWL resistors n. Therefore, it is necessary to develop a powerful test for non-existence of a solution in a given region (consisting of many linear regions) so that we can discard many linear regions containing no solution at an early stage of the algorithm.…”