A HYBRID POLYNOMIAL SYSTEM SOLVING METHOD FOR MIXED TRIGONOMETRIC POLYNOMIAL SYSTEMS.

Mixed trigonometric polynomial systems arise in many fields of science and engineering. Commonly, this class of systems is transformed into polynomial systems by variable substituting and 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 efficient hybrid method for solving polynomial systems coming from mixed trigonometric polynomial systems is presented. It combines the homotopy method, in which the homotopy is a combination of coefficient parameter homotopy and the random product homotopy, with decomposition, variable substitution, and reduction techniques. Numerical tests are given to show its effectiveness, and it is applied to solve a practical problem. [ABSTRACT FROM AUTHOR]