Algorithm(s) need for Bessel functions

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4 total messages Started by Liang-Wu Cai Mon, 25 Jan 1993 20:14

#1085

Author: Liang-Wu Cai
Date: Mon, 25 Jan 1993 20:14

23 lines
1363 bytes

Dear netter,

 I am in need (badly) of an accurate algorithm Bessel functions of various 
kinds with real argument and integer order. What I need actually is a 
algorithm which is able to provide the result with at least 7 significant 
digits for J_n (z) and Y_n (z) with n <=100 and z <= 100. Please note this
requires a relative error crition, though some absolute critera may be
incorperated with the only purpose to prevent possible underflows. The algoriths
may be in FORTRAN or C, or some easy-to-understant "psuedo-code".

The method in "Numerical Recipes" fails to give out any error information, and
collapes somewhere. I can't find any others. 

Since I need it badly, I may be required to write one for my own. So suggestions
on how to write scuh a function also welcome. 

Thanks in advance.

Please e-mail me at "cai@athena.mit.edu"


Liang-Wu Cai

Re: Algorithm(s) need for Bessel functions

#1087

Author: vaxinf
Date: Tue, 26 Jan 1993 10:09

33 lines
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In article <1993Jan25.201447.2082@athena.mit.edu>, cai@athena.mit.edu (Liang-Wu Cai) writes:
|>Xref: eratu.rz.uni-konstanz.de sci.math.num-analysis:4147 sci.engr:2316 sci.engr.mech:820
|>Newsgroups: sci.math.num-analysis,sci.engr,sci.engr.mech
|>Path: eratu.rz.uni-konstanz.de!news.belwue.de!ira.uka.de!sol.ctr.columbia.edu!spool.mu.edu!enterpoop.mit.edu!bloom-picayune.mit.edu!athena.mit.edu!cai
|>From: cai@athena.mit.edu (Liang-Wu Cai)
|>Subject: Algorithm(s) need for Bessel functions
|>Message-ID: <1993Jan25.201447.2082@athena.mit.edu>
|>Sender: news@athena.mit.edu (News system)
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|>Organization: Massachusetts Institute of Technology
|>Date: Mon, 25 Jan 1993 20:14:47 GMT
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|>
|>
|>Dear netter,
|>
|> I am in need (badly) of an accurate algorithm Bessel functions of various 
|>kinds with real argument and integer order. What I need actually is a 
|>algorithm which is able to provide the result with at least 7 significant 
|>digits for J_n (z) and Y_n (z) with n <=100 and z <= 100.

Look into Abromowitz/Stegun Handbook of Mathamatical Functions:

1.) set j(100)=0
2.) set j(99)=1
3.) do recursion to j(0)
4.) calculate the true j(0) in order to define a normalisation faktor
5.) Multiply all value with that factor

You get all values J(0)...j(100) in that way.

Eberhard Heuser-Hofmann

Re: Algorithm(s) need for Bessel functions

#1100

Author: Tilo Levante
Date: Tue, 26 Jan 1993 17:29

34 lines
1892 bytes

In article <1993Jan26.100935.113272@eratu.rz.uni-konstanz.de>, vaxinf@V36.CHEMIE.UNI-KONSTANZ.DE () writes:
|> 
|> In article <1993Jan25.201447.2082@athena.mit.edu>, cai@athena.mit.edu (Liang-Wu Cai) writes:
|> |>Dear netter,
|> |>
|> |> I am in need (badly) of an accurate algorithm Bessel functions of various 
|> |>kinds with real argument and integer order. What I need actually is a 
|> |>algorithm which is able to provide the result with at least 7 significant 
|> |>digits for J_n (z) and Y_n (z) with n <=100 and z <= 100.
|> 
|> Look into Abromowitz/Stegun Handbook of Mathamatical Functions:
|> 
|> 1.) set j(100)=0
|> 2.) set j(99)=1
|> 3.) do recursion to j(0)
|> 4.) calculate the true j(0) in order to define a normalisation faktor
|> 5.) Multiply all value with that factor
|> 
|> You get all values J(0)...j(100) in that way.
|> 
|> Eberhard Heuser-Hofmann

This algorithm (Miller algorithm)
is based on a recurrence relation for besselfunctions.
You can find a detailed description in 

 Computation with recurrence relations
 / Jet Wimp
 Boston a.o. : Pitman, 1984
 XII, 310 p. : tab. ; 24 cm
 (Applicable mathematics series)
 ISBN 0-273-08508-5

Tilo

Re: Algorithm(s) need for Bessel functions

#1123

Author: Darth Vader
Date: Thu, 28 Jan 1993 17:45

7 lines
1050 bytes

Hi,
	I beleive there are some routines for bessel functions available
in the TOMS package. Try netlib@research.att.com for the list of
functions available in the TOMS package. You can send for index to the
machine or you can do an anon ftp to the site.

D.V

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