基于概率投点算法在积分近似计算中的应用

On the Application of the Probability-based Projected Point Algorithm in Integral Approximation Calculation

基于概率的随机试验和随机事件近似计算积分值,是一个重要的积分近似计算思路,这种思路相比逼近法计算数值积分要简单易行,而且精度也能保证.投点算法的使用需要函数最值作为前提,所以首先给出了函数最值的计算机计算,然后以投点算法为基础依次探讨了[0,1]区间和[a,b]区间上的积分的近似计算,最后把前面这两种积分的计算推广到了多维积分的情况,对于每种情况都给出了计算机模拟.

The approximate calculation of integral values on the basis of the randomized trials and random events of probability is an important idea for integral approximate calculation. The said calculation method, compared with the approximation method, is simple and easy to handle in calculating numerical integration and with reliable accuracy. The use of projected point algorithm presupposes a function maximum value as a prerequisite, so first the computer calculation of the function maximum value is presented, then on the basis of the projected point algorithm the approximation integration calculation is put under discussion on the interval and the interval by turn, and at last the above two methods for integral calculation are popularized to cases of multi-dimensional integrationand for each case a computer simulation is provided.