Implementations
In the Matlab Optimization Toolbox, the fminunc function uses BFGS with cubic line search when the problem size is set to "medium scale." The GSL implements BFGS as gsl_multimin_fdfminimizer_vector_bfgs2. In SciPy, the scipy.optimize.fmin_bfgs function implements BFGS. It is also possible to run BFGS using any of the L-BFGS algorithms by setting the parameter L to a very large number.
A high-precision arithmetic version of BFGS (pBFGS), implemented in C++ and integrated with the high-precision arithmetic package ARPREC is robust against the numerical instability (e.g. round-off errors).
Read more about this topic: BFGS Method