蒙特卡罗方法计算定积分的进一步讨论

Further Discussing of Using Monte-Carlo Method to Calculate Definite Integral

介绍了蒙特卡罗方法计算定积分的原理和方法.给出了用蒙特卡罗方法计算定积分的一个简单证明,从而揭示了蒙特卡罗方法和定积分定义间的内在联系.针对蒙特卡罗方法收敛慢的特点,提出将蒙特卡罗方法与相应的数值计算方法相结合,提高计算结果的精度.此外,将蒙特卡罗方法推广到反常积分上去.

This paper introduces the principle and method of using Monte-Carlo method to calculate multiple integrals. It gives a simple prove for using Monte-Carlo method to calculate definite integral, hence reveals the internal connection between Monte- Carlo method and the definition of definite integral . Since Monte-Carlo method＇s convergence rate is slow, this paper also puts forward that Monte-Carlo method should be combined with numerical analysis method to improve precision of calculate result. Lastly, it popularizes Monte-Carlo method to calculate improper integral.