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Re: [Help-gsl] Hankel transform and Bessel functions zeros

From: M J Carley
Subject: Re: [Help-gsl] Hankel transform and Bessel functions zeros
Date: Mon, 26 Sep 2011 15:47:26 +0100 (BST)

On Tue, 20 Sep 2011, Brian Gough wrote:

At Fri, 26 Aug 2011 11:28:14 +0100 (BST),
Michael Carley wrote:
It seems to me that it might be useful to include an implementation of the
root finding algorithm in GSL since it could be used for a wide range of
special functions, not just Bessel functions, and would also improve the
accuracy of the Hankel transform, and I would be happy to recode my
implementation to GSL standards or pass it on to someone else who could do

Thanks for the email, and sorry for the delay in replying.  Can you
give me an idea of how much of a drop-in replacement this would be --
is it a case of polishing the existing roots or is it a completely new
way of calculating them?

Polishing the existing roots would be a good quick fix, but what I am talking about is a general method for computing a sequence of roots of a special function in O(N) time. This is a completely new way of calcuating them and could be used for zeros of plenty of other functions. Originally, it was developed for calculating roots for Gaussian quadrature rules so it applies to the various classical special functions used for quadrature.

`Al vero filosofo ogni terreno e' patria.'

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