Path Following Circuits ― SPICE-Oriented Numerical Methods Where Formulas are Described by Circuits―

摘要

Path following circuits (PFC's) are circuits for solving nonlinear problems on the circuit simulator SPICE. In the method of PFC's, formulas of numerical methods are described by circuits, which are solved by SPICE. Using PFC's, numerical analysis without programming is possible, and various techniques implemented in SPICE will make the numerical analysis very efficient. In this paper, we apply the PFC's of the homotopy method to various nonlinear problems (excluding circuit analysis) where the homotopy method is proven to be globally convergent; namely, we apply the method to fixed-point problems, linear programming problems, and nonlinear programming problems. This approach may give a new possibility to the fields of applied mathematics and operations research. Moreover, this approach makes SPICE applicable to a broader class of scientific problems.