基于改进拟牛顿法求解非线性方程组

Solving Nonlinear Systems Via Improved Quasi-Newton Methods

为解决拟牛顿法求解非线性方程组时表现出的全局搜素能力差、耗时久、易发散等问题,基于机器学习的思想对传统拟牛顿法进行改进,机器学习思想会根据拟牛顿法初始搜索过程进行机器学习,对学习函数和决策函数进行训练,可大大提升计算速度和计算精度.同常用的非线性方程组进行求解算法进行比较,在全局搜索能力、计算精度、计算速度三个层面揭示改进算法的适用性和优越性.

In order to solve the problem of global search ability is poor, time-consuming, easy divergence and other issues in the process of solving nonlinear systems via Quasi-Newton methods, this reserach improves the traditional Quasi-Newton method based on the idea of machine learning： Machine learning theory will be based on the initial search process of Quasi-Newton method for machine learning, to train the learning function and decision function, it can greatly improve the calculation speed and accuracy. Compared with the algorithm for solving system of nonlinear systems which are commonly used in the present, the result shows that the algorithm in tiis paper is superior to other algorithms in terms of global search capability, computational accuracy and computational speed.