[Bug-gsl] [bug #45782] Feature request: Make derivative epsilon configurable

[Alexander Voigt]

URL:
  <http://savannah.gnu.org/bugs/?45782>

                 Summary: Feature request: Make derivative epsilon
configurable
                 Project: GNU Scientific Library
            Submitted by: avoigt
            Submitted on: Mo 17 Aug 2015 17:38:43 GMT
                Category: Accuracy problem
                Severity: 3 - Normal
        Operating System: all
                  Status: None
             Assigned to: None
             Open/Closed: Open
                 Release: all
         Discussion Lock: Any

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Details:

Dear GSL hackers,

for my research project I'm using the GSL multiroot solvers (w/o derivative). 
However, I stumbled upon a numerical problem:

The function that I'm passing to the multiroot solvers cannot be evaluated
very precisely.  I.e. there is a numerical imprecision in the function
evaluation of the order 1e-5.

When I pass this function to the multiroot solvers (w/o providing a function
for the derivative), one of the first things the solver does is to calculate
the Jacobian.  For the calculation of the Jacobian matrix different
derivatives of the function have to be calculated numerically.  For the
calculation of these derivatives a hard-coded epsilon of GSL_SQRT_DBL_EPSILON
= 1.4901161193847656e-08 is used.  This value is too small for my application,
because it is smaller than the numerical imprecision of the function
evaluation.  In my case 1e-4 would be optimal.

For this reason I'd like to request the following feature:  Please make the
epsilon, which is used in the calculation of the Jacobian, configurable.

Best regards,
Alexander Voigt





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