基于Prony-like方法的第一类贝塞尔函数逼近

On evaluation of Bessel functions of the first kind via Prony-like methods

贝塞尔函数的数值逼近既有重要的理论意义,又在数学、物理学、工程等各个领域有着广泛的应用.研究整数阶第一类贝塞尔函数的数值逼近,基于Prony方法,采用不同三角函数(正弦、余弦)形式的Prony-like方法进行逼近.通过在符号计算软件Maple中对函数进行数值实验,分析不同整数阶的第一类贝塞尔函数在不同自变量区间上的数值逼近,将Prony-like方法的实验结果与基于傅里叶级数展开的方法进行对比,发现Prony-like方法的逼近效果远优于基于傅里叶级数的方法.

Numerical approximations of Bessel functions are both of important theoretical significance and widely applied in mathematics,physics,engineering.In this work,we apply two variants of Prony's method on Bessel functions of the first kind of integer order.The Prony-like methods in cosine or sine version yield approximations as sums of sinusoidal functions of Bessel functions of the first kind of integer order.In the symbolic computation software Maple,we compute the approximations for different orders and over different intervals,and compare these approximations with those obtained through the Fourier method.Experiments show that Prony-like methods perform much better than the Fourier method.