求解非线性代数方程组的一种建议方法

A Recommendable Method to Solve Nonlinear Algebraic Equations

飞行动力学研究中常遇到求解非线性代数方程组的问题。现提出一种求解实函数非线性代数方程组的组合迭代方法，以多步交替使用的方式将梯度下降法和拟牛顿选代法结合起来，综合两者的优点，组成一种对大范围内偏离精确解的任意初值均能收敛、且有一定收敛速度的迭代法。通过算例，对三种方法进行了对比和分析，计算结果证明，该方法是优越的。

The solution of nonlinear algebraic equations is usually met in the study of flight dynamics. A combinatorial iteration method to solve the nonlinear algebraic equations is put forward in this paper. The method combines the gradient method with quasi-Newton method and abstracts the advantages from the both methods, using them steps by steps alternately. The combinatorial method can be converged to any initial values that has long distance to the precise values and has proper speed for convergence.