[Bug-gsl] [bug #39713] roots/secant.c "derivative value is not finite" for a good guess

[Brian Gladman]

Follow-up Comment #3, bug #39713 (project gsl):

The section within secant.c in which the root position, the function value and
the derivative value are updated is:

  x_new = x - (f / df);

  f_new = GSL_FN_FDF_EVAL_F(fdf, x_new) ;
  df_new = (f_new - f) / (x_new - x) ;

  *root = x_new ;

Although it involves an additional multiplication, I think this may be safer:

  x_new = x - (f / df);

  f_new = GSL_FN_FDF_EVAL_F(fdf, x_new) ;
  df_new = df * (1.0 - f_new / f) ;

  *root = x_new;

since it avoids the potential problem of x_new and x being the same because (f
/ df) is too small to change x when it is subtracted.  Also, since the
algorithm shouldn't presumably be entered with f = 0, the division f_new / f
should not cause a divide by zero problem.


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