An efficient algorithm is proposed for finding all DC solutions of nonlinear circuits. This algorithm is based on interval analysis and a new strategy called LP narrowing. In the LP narrowing strategy, boxes (n-dimensional rectangles in the solution domain) containing no solution are excluded, and boxes containing solutions are narrowed so that no solution is lost by using linear programming techniques. Since the LP narrowing is very powerful, all solutions can be found very efficiently. By numerical examples, it is shown that the proposed algorithm could find all solutions of large-scale systems of nonlinear circuit equations in practical computation time.

Finding DC operating points of nonlinear circuits is an important problem in circuit simulation. The Newton-Raphson method employed in SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. There are several types of homotopy methods, one of which succeeded in solving bipolar analog circuits with more than 20000 elements with the theoretical guarantee of global convergence. In this paper, an improved version of the homotopy method is proposed that can find DC operating points of practical nonlinear circuits smoothly and efficiently. It is also shown that the proposed method can be easily implemented on SPICE without programming.

Recently, an efficient homotopy method termed the variable gain Newton homotopy (VGNH) method has been proposed for finding DC operating points of nonlinear circuits. This method is not only very efficient but also globally convergent for any initial point. However, the programming of sophisticated homotopy methods is often difficult for non-experts or beginners. In this paper, we propose an effective method for implementing the VGNH method on SPICE. By this method, we can implement a "sophisticated VGNH method with various efficient techniques" "easily" "without programming," "although we do not know the homotopy method well"

An efficient algorithm is proposed for finding all solutions of piecewise-linear (PWL) resistive circuits using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of PWL equations in a given region. In the LP test, the system of PWL equations is transformed in to an LP problem, to which the simplex method is applied. Such an LP problem is obtained by surrounding the PWL functions by rectangles. In this paper, we introduce the dual simplex method to the LP test, which makes the average number of pivotings per region much smaller (less than one, for example) and makes the algorithm very efficient.

A globally convergent algorithm that is also quadratically convergent for solving bipolar transistor networks is proposed. The algorithm is based on the homotopy method using a rectangular subdivision. Since the algorithm uses rectangles, it is much more efficient than the conventional simplicial-type algorithms. It is shown that the algorithm is globally convergent for a general class of nonlinear resistive networks. Here, the term globally convergent means that a starting point which leads to the solution can be obtained easily. An efficient acceleration technique which improves the local convergence speed of the rectangular algorithm is proposed. By this technique, the sequence of the approximate solutions generated by the algorithm converges to the exact solution quadratically. Also, in this case the computational work involved in each iteration is almost identical to that of Newton's method. Therefore, the algorithm becomes as efficient as Newton's method when it arrives sufficiently close to the solution. It is also shown that sparse-matrix techniques can be introduced to the rectangular algorithm, and the partial linearity of the system of equations can be exploited to improve the computational efficiency. Some numerical examples are also given in order to demonstrate the effectiveness of the proposed algorithm.>