A new algorithm is proposed for finding all solutions of piecewise-linear resistive circuits using separable programming. In this algorithm, the problem of finding all solutions is formulated as a separable programming problem, and it is solved by the modified simplex method using the restricted-basis entry rule. Since the modified simplex method finds one solution per application, the proposed algorithm can find all solutions efficiently. Numerical examples are given to confirm the effectiveness of the proposed algorithm.

Recently, efficient algorithms have been proposed for finding all characteristic curves of one-port piecewise-linear resistive circuits. Using these algorithms, a middle scale one-port circuit can be represented by a piecewise-linear resistor that is neither voltage nor current controlled. In this letter, an efficient algorithm is proposed for finding all dc operating points of piecewise-linear circuits containing such neither voltage nor current controlled resistors.

An efficient algorithm is proposed for finding all solutions of piecewise-linear resistive circuits containing bipolar transistors. This algorithm is based on a powerful test (termed the LP test) for nonexistence of a solution in a given region using linear programming (LP). In the LP test, an LP problem is formulated by surrounding the exponential functions in the Ebers-Moll model by right-angled triangles, and it is solved by LP, for example, by the simplex method. In this paper, it is shown that the LP test can be performed by the dual simplex method, which makes the number of pivotings much smaller. Effectiveness of the proposed technique is confirmed by numerical examples.

An efficient algorithm is proposed for finding all dc solutions of piecewise-linear (PWL) circuits. This algorithm is based on a powerful test (termed the LP test) for nonexistence of a solution to a system of PWL equations in a given region using the dual simplex method. The proposed algorithm also uses a special technique that decreases the number of regions on which the LP test is performed. By numerical examples, it is shown that the proposed algorithm could find all solutions of large scale problems, including those where the number of variables is 500 and the number of linear regions is 10500, in practical computation time.

Recently, an efficient algorithm has been proposed for finding all solutions of systems of nonlinear equations using inverses of approximate Jacobian matrices. In this letter, an effective technique is proposed for improving the computational efficiency of the algorithm with a little bit of computational effort.

We consider an algorithm for finding all solutions in order to clarify all the stable equilibrium points of a hysteresis neural network. The algorithm includes sign test, linear programming test and a novel subroutine that divides the solution domain efficiently. Using the hysteresis network, we synthesize an associative memory whose cross connection parameters are trinalized. Applying the algorithm to the case where 10 desired memories are stored into 77 cells network, we have clarified all the solutions. Especially, we have confirmed that no spurious memory exists as the trinalization is suitable.