布谷鸟牛顿迭代算法求解非线性方程组

Cuckoo Newton Iterative Algorithm for Solving Nonlinear Equations

摘要: 近年来，非线性方程组问题越来越多的出现在科学与工程计算领域中。例如机器学习、人工智能、金融计算、石油地质探测、卫星轨道预测等各个领域都涉及到了非线性方程组求解的问题，如何有效快速的求解各类非线性方程组问题受到人们的普遍关注。其中牛顿迭代是求解非线性方程(组)的一个重要方法。本文首先利用布谷鸟搜索算法得到初值，然后利用牛顿迭代法求解非线性方程组。理论分析了这些格式的收敛阶。最后给出一些数值算例对三种迭代格式进行了分析比较，验证了理论并分析了结论。

Abstract: In recent years, the problem of nonlinear equations appears more and more in the field of science and engineering calculation. Such as, machine learning, artificial intelligence, financial computing, petroleum geological exploration, satellite orbit prediction and other fields are involved in nonlinear equations. How to effectively and quickly solve various nonlinear equations has been widely concerned by many researchers. Newton’s method is an important method for solving nonlinear equations. The method in this paper is to use the variation of Newton’s method to improve the order of convergence, and combine with cuckoo algorithm to find a better initial point, so as to achieve the purpose of solving the nonlinear equations. Finally, some numerical examples are used to analyze and compare the different iterative schemes, and support the method.