多重积分的平均值估计算法的改进与仿真研究

Simulation on Calculating Multiple Integrals Based on Improved Average Algorithm

关于多重积分的近似计算优化问题,针对传统平均值估计法在多重积分近似计算过程中受到积分维数和积分区域形状的限制问题,提出了一种改进的平均值估计算法。在传统平均值估计法的基础上,通过给出描述积分区域特性的几何条件,将多重积分转化为累次积分,同时将均匀分布与积分区域相结合的方法对原算法进行了改进。一个实例计算过程表明改进的算法较好地克服了传统平均值估计法的不足,在保证了计算精度的同时将积分计算推广到了不规则积分区域的高维积分的数值计算。

Study on approximate calculation of multiple integrals. The traditional average algorithm is limited to the integral area and the number of dimensions. In order to improve the algorithm, the geometrical characteristics of integral area were described. The calculation multipled integrals should be converted to calculation repested integrals and the uniform distribution should be combined with the area of integral area. The improved algorithm is particularly suited to solve the problems of multiple dimensions and irregular geometric shapes. One practical example shows that the improved algorithm is simple, effective and more practical.