摘要
首先推导了Buffon投针问题中的针长与平行线间距比值和圆周率π的估计精度之间的关系,然后应用蒙特卡洛方法验证了理论结果.发现除了随机试验次数以外,针长与平行线间距比值是影响圆周率π估计精度的重要因素,针长的长度增加能够提高圆周率π估计精度.因此在应用蒙特卡洛方法时,适当设定模型可控制参数能够使估计精度成倍提高.
Firstly,It has been deduced that the theoretical relations between precision of estimatingπand the ratio of the length of the needle to parallel line spacing in Buffon＇s Needle.Then the results of the Monte Carlo method have verified the theoretical correctness. In addition to the number of simulations,the ratio of the length of the needle to parallel line spacing is another important factor which affects the accuracy of estimatingπ,and the simulating precision ofπcan be improved with the increasing of the length of the needle. Therefore,in the application of Monte Carlo methods,the appropriate hypothesis of model parameter values can enhance precision and convergence rate of estimator.
出处
《数学的实践与认识》
CSCD
北大核心
2010年第22期243-247,共5页
Mathematics in Practice and Theory
基金
新疆维吾尔自治区高校研青年项目(编号XJEDU2008S54)
新疆财经大学校级课题项目(编号08XYB006)
