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Re: [Help-gsl] Bessel functions and continued fractions

From: Brian Gough
Subject: Re: [Help-gsl] Bessel functions and continued fractions
Date: Fri, 06 Aug 2010 09:44:51 +0100
User-agent: Wanderlust/2.15.6 (Almost Unreal) Emacs/23.2 Mule/6.0 (HANACHIRUSATO)

At Thu, 29 Jul 2010 12:42:57 +0100, Jonny Taylor wrote:
> Is there anybody where who knows the ins and outs of the Bessel
> function implementation in GSL? Under certain circumstances my code
> is spending over 90% of its time in gsl_sf_bessel_J_CF1. This occurs
> for large x<1000 and n<50. The time taken to evaluate the continued
> fraction grows with x.

Can you send a test case where it's really bad for adding to the test
suite (specfunc/test_bessel.c), I appreciate that it's a performance
problem rather than an accuracy problem but it's easiest to keep track
of it if it's in there.  Are the results actually accurate? Usually
these excessive numbers of iterations are a sign of poor convergence.

> Is there a reason that CF2 is not used in GSL? I don't know about
> the reasoning behind the implementation and the regimes where each
> of the various evaluation methods are used. Is there a reason for
> not using CF2 in the appropriate circumstances, or is it just that
> nobody has felt the need to implement it up to now?

I do not know about the choices behind it, the original author was
address@hidden  If you can make a CF2 patch which is faster and
passes the test suite that would be the way forward.

Brian Gough

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