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fsolve not finding correct answer

From: Aivo Jürgenson
Subject: fsolve not finding correct answer
Date: Sun, 11 Feb 2007 22:17:47 +0200 (EET)


I'm trying to use fsolve for finding unknown $k$ in a somewhat complex equation

        $ p = \int_{-k}^{k} f_B(y,\sigma) dy $

where f_B is the probability density function of "Bessel's" distribution and equals to


where besselk is the standard Octave function.

The problem is that the fsolve function doesn't do a very good job and sometimes gives "iteration is not making good progress" and therefore completely wrong answer as well.

The appropriate code is given in the atree_bessel_find_range.m file in the attachment. I'm using the 2.1.73-13 Debian package of Octave.

Anybody has some hints about how to persuade fsolve giving the correct answer or perhaps somebody could suggest a different function for solving the equation in the first place?

Aivo Jürgenson

Attachment: atree_bessel_find_range.m
Description: Text document

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