NDLI: Algorithm to Calculate a Large Number of Roots of the Cross-Product of Bessel Functions

Content Provider	IEEE Xplore Digital Library
Author	Sorolla, E. Mosig, J. R. Mattes, M.
Copyright Year	1963
Abstract	This paper describes an algorithm to calculate a large number of roots of the cross-product of Bessel functions and of their first derivatives. The algorithm initially finds the roots of the zeroth order using an auxiliary function that exhibits the same roots as the original cross-products but with better behavior for numerical root search with the Newton–Raphson algorithm. In order to find the roots for higher orders, the algorithm follows a pyramidal scheme using the interlacing property of the cross-product of Bessel functions. The algorithm shows globally convergent behavior for a large range of values of the argument and of the order of the Bessel functions. The roots can be computed to any precision, limited only by the computer implementation, and the convergence is attained in six iterations per root in average, showing a much better performance than previous works for the calculation of these roots.
Sponsorship	IEEE Antennas and Propagation Society
Starting Page	2180
Ending Page	2187
Page Count	8
File Size	2098428
File Format	PDF
ISSN	0018926X
Volume Number	61
Issue Number	4
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-04-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Electromagnetic waveguides Equations Mathematical model Convergence Indexes Electromagnetics Electromagnetic scattering Newton–Raphson Algorithm Bessel functions cross-product interlacing properties McMahon's expansion
Content Type	Text
Resource Type	Article
Subject	Condensed Matter Physics Electrical and Electronic Engineering

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