Simplicial fixed points algorithms for finding several solutions of nonlinear circuits

The fixed‐point algorithm is a method of obtaining the constructive solution of the system of nonlinear equations. the fixed‐point algorithms can roughly be divided into the differential method and the piecewise‐linear method. This paper adopts the fixed‐point algorithm based on piecewise linearization, which does not require considering the differentiability of the system of nonlinear equations, and shows a method for determining more than one solution of the n‐dimensional system of nonlinear equations. the homotopy defined on 0, ∞ × Rⁿ is used. to trace the solution curve of the homotopy, the special decomposition triangulation of 0, ∞ Rⁿ space is required. By providing a new triangulation of 0, ∞ × Rⁿ for Merrill's and Eaves‐Saigal's methods which are typical and based on piecewise linearization, those methods are extended from the methods of obtaining a single solution to the methods of obtaining more than one solution.