An efficient approach for finding all solutions based on submatrix estimation
Hidetoshi Kinoshita, Hideki Asai · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1996
Abstract Finding all solutions based on the piecewise‐linear search is one of the steadiest methods to solve the nonlinear equation. A feature of the method is that the local convergence problem is not involved. On the other hand, the number of region searches required even for a smallscale problem is tremendous. This paper proposes an efficient method for finding all solutions, restricting the problem to the anlayis of bipolar circuits. Based on the range of values that each variable can take and the liearity of the equation, the solution candidate regions are restricted by evaluating the existence possibility of the solution for each of the multiple subset variables. the submatrix is considered and the size is varied, and the efficiency of the solution search is improved by testing a large number of linear regions at the same time. The proposed method works especially effectively when the signal propagation in the circuit has a directivity or the subcircuits have high independencies. Finally, the effectiveness of the proposed method is shown through actual compution exemples.