华东师范大学学报(自然科学版) ›› 2019, Vol. 2019 ›› Issue (6): 42-60.doi: 10.3969/j.issn.1000-5641.2019.06.006

• 数学 • 上一篇    下一篇

基于Prony-like方法的第一类贝塞尔函数逼近

纪宇, 何一璇, 吴国群, 吴敏   

  1. 华东师范大学 上海市高可信计算重点实验室, 上海 200062
  • 收稿日期:2018-11-30 出版日期:2019-11-25 发布日期:2019-11-26
  • 通讯作者: 吴敏,女,副教授,主要研究方向为符号计算、数值计算.E-mail:mwu@sei.ecnu.edu.cn. E-mail:mwu@sei.ecnu.edu.cn
  • 作者简介:纪宇,女,硕士研究生,研究方向为数值计算、符号计算.E-mail:15526476747@163.com.
  • 基金资助:
    国家自然科学基金(11371143)

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

JI Yu, HE Yi-xuan, WU Guo-qun, WU Min   

  1. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China
  • Received:2018-11-30 Online:2019-11-25 Published:2019-11-26

摘要: 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.

关键词: 贝塞尔函数, Prony-like方法, 三角函数, 基于傅里叶级数展开, 数值逼近

Abstract: 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.

Key words: Bessel functions, Prony-like methods, trigonometric functions, Fourierbased method, numerical approximation

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