改进Monte Carlo算法在非线性方程组求解中的应用

Application of improved Monte Carlo method to solution of nonlinear equations

借鉴数值方法中梯度方法的思想,引进了广义负梯度方向的概念,给出了一种基于广义负梯度方向的Monte Carlo方法———GGMC方法.该方法保持了Monte Carlo算法的普适性和稳定性,并改善了原方法搜索的盲目性和随机性,提高了原方法的搜索效率,缩短了计算时间.将GGMC方法用于算例,收敛速度明显提高.

The concept of general gradient was introduced into the original Monte Carlo method, and an improved Monte Carlo method based on general negative gradient was proposed. The present method keeps the general suitability and stability of the original method, and overcomes the blindness and randomness of the original search method, so it improves the search efficiency and shortens the calculation time. A case study with the improved algorithm shows that the convergence speed is greatly improved.