fsolve not finding correct answer

[Aivo Jürgenson]

Hello,

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

        p=(1/(pi.*sigma)).*besselk(0,(abs(y)./sigma));

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

atree_bessel_find_range.m
Description: Text document