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Titolo:
ELF and GNOME: Two tiny codes to evaluate the real zeros of the Bessel functions of the first kind for real orders
Autore:
Segura, J; Gil, A;
Indirizzi:
Univ Miguel Hernandez, Inst Bioingn, Alicante 03202, Spain Univ Miguel Hernandez Alicante Spain 03202 ioingn, Alicante 03202, Spain Ctr Wiskunde & Informat, NL-1098 SJ Amsterdam, Netherlands Ctr Wiskunde & Informat Amsterdam Netherlands NL-1098 SJ am, Netherlands
Titolo Testata:
COMPUTER PHYSICS COMMUNICATIONS
fascicolo: 3, volume: 117, anno: 1999,
pagine: 250 - 262
SICI:
0010-4655(199903)117:3<250:EAGTTC>2.0.ZU;2-O
Fonte:
ISI
Lingua:
ENG
Keywords:
first kind Bessel functions; zeros of Bessel functions; Newton method;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
11
Recensione:
Indirizzi per estratti:
Indirizzo: Segura, J Univiniguel Hernandez, Inst Bioingn, Edificio La Galia, Alicante03202, Spa Univ Miguel Hernandez Edificio La Galia Alicante Spain 03202 pa
Citazione:
J. Segura e A. Gil, "ELF and GNOME: Two tiny codes to evaluate the real zeros of the Bessel functions of the first kind for real orders", COMP PHYS C, 117(3), 1999, pp. 250-262

Abstract

Two codes to evaluate the real zeros (j(v,s)) of the Bessel functions of the first kind J(v)(x) for real orders v are presented. The codes are based on a Newton-Raphson iteration over the monotonic function f(v)(x) = x(2v-1)J(v)(x)/J(v-1) (x). The code ELF is a remarkably short program for finding, given any startingvalue x(0) > 0 and any real order, the zero of J(v)(x) in the neighborhoodof x(0) (x(0) and the zero in the same branch of f(v)(x)). GNOME is amodification of ELF for finding the zeros of J(v)(x) inside a given interval [x(min), x(max)]; for simplicity, we restrict the code GNOME to work for v > -1, which is the region of greatest practical use, where all the zeros of J(v)(x) are real. The method is especially efficient for moderate values of v and for small zeros, where asymptotic expansions tend to fail and, besides, contrary to existing algorithms; enables the search of the real zeros for real orders, including negative orders. (C) 1999 Elsevier Science B.V.

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Documento generato il 29/05/20 alle ore 17:04:46