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.

This paper describes how the symmetry of a three-phase circuit prevents the symmetric modes of several subharmonic oscillations. First, we make mathematically it clear that the generation of symmetrical 1/3l-subharmonic oscillations (l=1,2,) are impossible in the three-phase circuit. As far as 1/(3l+1)-subharmonic oscillations (l=1,2,) and 1/(3l+2)-subharmonic oscillations (l=0,1,) are concerned, the former in negative-phase sequence and the latter in positive-phase sequence are shown to be impossible. Further, in order to confirm the above results, we apply the method of interval analysis to the circuit equations and obtain all steady state solutions with unsymmetric modes.

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.

Recently, an efficient algorithm has been proposed for finding all solutions of systems of nonlinear equations using linear programming. In this algorithm, linear programming problems are formulated by surrounding component nonlinear functions by rectangles. In this letter, it is shown that weakly nonlinear functions can be surrounded by smaller rectangles, which makes the algorithm very efficient.

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 bipolar transistor circuits. This algorithm is based on a simple test that checks the nonexistence of a solution using linear programming. In this test, right-angled triangles are used for surrounding exponential functions of the Ebers-Moll model, by which the number of inequality constraints decreases and the test becomes efficient and powerful.

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.