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.

An efficient algorithm is proposed for finding all solutions of piecewise-linear resistive circuits The algorithm is based on the idea of "contraction" of the solution domain using a sign test. The proposed algorithm is efficient because many large super-regions containing no solution are eliminated in early steps.

An efficient algorithm is given for finding all solutions of piecewise-linear resistive circuits containing nonseparable transistor models such as the Gummel-Poon model or the Shichman-Hodges model. The proposed algorithm is simple and can be easily programmed using recursive functions.

An efficient algorithm is presented for finding all solutions of piecewise-linear resistive circuits containing sophisticated transistor models such as the Gummel-Poon model or the Shichman-Hodges model. When a circuit contains these nonseparable models, the hybrid equation describing the circuit takes a special structure termed pairwise-separability (or tuplewise-separability). This structure is effectively exploited in the new algorithm. A numerical example is given, and it is shown that all solutions are computed very rapidly.

Recently, efficient algorithms that exploit the separability of nonlinear mappings have been proposed for finding all solutions of piecewise-linear resistive circuits. In this letter, it is shown that these algorithms can be extended to circuits containing piecewise-linear resistors that are neither voltage nor current controlled. Using the parametric representation for these resistors, the circuits can be described by systems of nonlinear equations with separable mappings. This separability is effectively exploited in finding all solutions. A numerical example is given, and it is demonstrated that all solutions are computed very rapidly by the new algorithm.

An efficient algorithm is presented for finding all solutions of piecewise-linear resistive circuits. In this algorithm, a simple sign test is performed to eliminate many linear regions that do not contain a solution. This makes the number of simultaneous linear equations to be solved much smaller. This test, in its original form, is applied to each linear region; but this is time-consuming because the number of linear regions is generally very large. In this paper, it is shown that the sign test can be applied to super-regions consisting of adjacent linear regions. Therefore, many linear regions are discarded at the same time, and the computational efficiency of the algorithm is substantially improved. The branch-and-bound method is used in applying the sign test to super-regions. Some numerical examples are given, and it is shown that all solutions are computed very rapidly. The proposed algorithm is simple, efficient, and can be easily programmed.

An efficient algorithm is presented for finding all solutions of piecewise-linear resistive circuits. In this algorithm, a simple sign test is performed to eliminate many linear regions that do not contain a solution. Therefore, the number of simultaneous linear equations to be solved is substantially decreased. This test, in its original form, requires O(Ln2) additions and comparisons in the worst case, where n is the number of variables and L is the number of linear regions. In this paper, an effective technique is proposed that reduces the computational complexity of the sign test to O(Ln). Some numerical examples are given, and it is shown that all solutions can be computed very efficiently. The proposed algorithm is simple and can be easily programmed by using recursive functions.