直接多胞体同伦方法求解混合三角多项式方程组

DIRECT POLYHEDRAL HOMOTOPY METHODS FOR SOLVING MIXED TRIGONOMETRIC POLYNOMIAL SYSTEMS

混合三角多项式方程组是科学工程计算中常见的一类非线性方程组,它的每项由一部分变元及另一部分变元的三角函数构成.文章主要考虑利用直接多胞体同伦方法求解混合三角多项式方程组.数值结果表明文中的方法优于已有的求混合三角多项式方程组全部解的数值方法.

A mixed trigonometric polynomial system, which rather frequently occurs in applications, is a polynomial system whose monomial is mixed by some variables and sine and cosine functions applied to the other variables. In this paper; the direct polyhedral homotopy method is applied to solve this class of systems, and numeri- cal results show that this new method is more efficient than the existent numerical methods for finding all isolated solutions of a mixed trigonometric polynomial system.