Evaluation of some algorithms and programs for the computation of integer-order Bessel functions of the first and second kind with complex arguments

Author

du Toit, C.F.

Author_Institution

Dept. of Electr. & Electron. Eng., Stellenbosch Univ., South Africa

Volume

35

Issue

3

fYear

1993

fDate

6/1/1993 12:00:00 AM

Firstpage

19

Lastpage

25

Abstract

The efficiency and accuracy of a few available algorithms for the computation of integer-order Bessel functions are considered. First, the computation of integer-order Bessel functions of the first kind, using the fast Fourier transform (FFT) algorithm as opposed to recurrence techniques, is investigated. It is shown that recurrence techniques are superior to the FFT technique, both in accuracy and speed. An algorithm suggested in the literature and used in commercially available software, specifically MATLAB 3.5 and MATHEMATICA 1.2, for computing integer-order Bessel functions of the second kind is revealed to be erroneous by comparing these routines with an algorithm developed by the author. It is shown that catastrophic errors result from using the erroneous algorithm to compute high-order Bessel functions with nonreal arguments.<>

Keywords

Bessel functions; fast Fourier transforms; mathematics computing; FFT algorithm; MATHEMATICA 1.2; MATLAB 3.5; algorithms; catastrophic errors; complex arguments; fast Fourier transform; first kind Bessel functions; integer-order Bessel functions; nonreal arguments; recurrence techniques; second kind Bessel functions; software; Africa; Difference equations; Fast Fourier transforms; MATLAB; Physics computing; Software algorithms; Stability; Turning;

fLanguage

English

Journal_Title

Antennas and Propagation Magazine, IEEE

Publisher

ieee

ISSN

1045-9243

Type

jour

DOI

10.1109/74.250131

Filename

250131