同伦迭代法的研究及其应用于机构学问题的求解

On the Homotopy Iteration Method and Its Application in the Mechanism Problems

通过分析多项式映射同伦函数零点集的特性,提出了一种改进路径跟踪方案的同伦迭代法,并论证了同伦迭代法求解非线性多项式方程组的可行性和可靠性,说明了该方法解高亏欠度多项式方程组时具有很高的计算效率。

Based on the analysis of the zero set characteristics of the nonlinear polynomial mapping homotopy function, a homotopy iteration method with an improved homotopy tracking scheme is proposed in this paper, and the feasibility and reliability of the homotopy iteration method for solving nonlinear polynomial systems is proved. The proposed method possesses a high efficiency in solving the high deficient polynomial systems. Numerical examples of mechanism problems demonstrate the efficiency and reliability of the method.