拉普拉斯逼近方法在复杂函数积分中的应用

Application of Laplace Approximation Method in Complex Function Integration

在常见的积分计算问题中,复杂函数的积分通常难以计算或是计算过程复杂,计算时间长.拉普拉斯逼近方法通过将复杂函数进行二阶泰勒展开,将满足一定条件的被积函数近似为正态分布密度函数的形式,并对其进行积分.从而求解出复杂函数积分的近似结果.文章基于正态分布良好的计算性质,通过实例分析拉普拉斯逼近方法在复杂函数积分中的应用,验证了拉普拉斯逼近方法具有计算方便,快捷,并且逼近结果较为精确的特点.

In the common integral calculation problem,the integral of complex functions is usually difficult to calculate or the calculation process is complicated and the calculation time is long.The Laplace approximation method approximates the integrand function satisfying certain conditions to a normal distribution by performing a second-order Taylor expansion of the complex function,and integrates the corresponding normal distribution density function to solve the approximate result of complex function integral.Due to the good computational properties of normal distribution,the application of Laplace approximation method in complex function integration is considered.The analysis of several examples shows that the Laplace approximation method is convenient,fast,and accurate.