Abstract: A hybrid algorithm for solving nonlinear equations is proposed in this paper． It has well combined their advantages of PSO and quasi-Newton method．The hybrid algorithm has sufficiently displayed the characteristics of PSO’s group searching and quasi-Newton method’s local strong searching． At the same time，it effectively overcomes the problem of high sensitivity to initial point of quasi-Newton method and shortcoming of PSO which reduces the searching efficiency in later period． Numerical experiments show that the hybrid algorithm has extremely stability，high convergence rate and precision．

Key words: nonlinear equations, Particle Swarm Optimization, quasi-Newton method

摘要： 结合粒子群算法和拟牛顿法的优点，提出了一种用于求解非线性方程组的混合算法。该混合算法充分发挥了粒子群算法的群体搜索性和拟牛顿法的局部细致搜索性，同时也克服了粒子群算法后期搜索效率降低和拟牛顿法对初始点敏感的缺陷。数值实验表明所设计的混合算法有极好的稳定性和较高的收敛速度和精度。

关键词: 非线性方程组, 粒子群算法, 拟牛顿法