A HYBRID POLYNOMIAL SYSTEM SOLVING METHOD FORMIXED TRIGONOMETRIC POLYNOMIAL SYSTEMS

摘要

Mixed trigonometric polynomial systems arise in many fields of science and engineer-ing. Commonly, this class of systems is transformed into polynomial systems by variable substitutingand adding some quadratic equations, and then solved by some polynomial system solving method.In this paper, by exploiting the special structure of the additional quadratic equations, an efficienthybrid method for solving polynomial systems coming from mixed trigonometric polynomial sys-tems is presented. It combines the homotopy method, in which the homotopy is a combination ofcoefficient parameter homotopy and the random product homotopy, with decomposition, variablesubstitution, and reduction techniques. Numerical tests are given to show its effectiveness, and it isapplied to solve a practical problem.