一类非线性超定方程组数值解法的研究

The Study of Numerical Solutions to a Class of Overdetermined System of Nonlinear Equations

本文介绍求解非线性超定方程组的4种数值方法,改进穷举法和蒙特卡洛算法,提出蒙特卡洛一穷举混合算法.应用这些数值方法求解太阳影子定位技术中提出的非线性超定方程组,根据数值试验结果分析各算法的优缺点;最后通过数值实例,比较各算法的求解时间和精度,验证各算法的有效性和蒙特卡洛一穷举混合算法的高效性.

In this paper four numerical methods for solving the overdetermined system of nonlinear equations are introduced.The Enumeration method and the Monte Carlo method are improved and combined into a Monte Carlo--Enumeration method.These numerical methods are applied to solve the overdetermined system of nonlinear equations which established at the base of the technology for positioning with the shadow of sun, advantages and disadvantages of each algorithm is analyzed according to the results of numerical experiments. At last,the computing time and accuracy of each algorithm are compared with numerical examples,the efficiency of each method and the high efficiency of Monte Carlo--Enumeration method are verified.