A Method for Computing All Solutions to Systems of Polynomials Equations

Abstract

Small polynomial systems of equations arise in many apphcations areas: computer-aided design, mechanical design, chemical kinetics modeling, and nonlinear circuit analysis. Use of local iterative methods, such as Newton's method, can be a hit-or-miss process. Purely algebraic schemes, such as the method of resultants, can lead to severe numerical difficulties. Imbedding methods provide the most reliable techniques for computing all solutions to small polynomial systems. One such method is described and computational experience with it is reported on. © 1983, ACM. All rights reserved.