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The following functions drive the iteration of each algorithm. Each
function performs one iteration to update the state of any solver of the
corresponding type. The same functions work for all solvers so that
different methods can be substituted at runtime without modifications to
the code.
 Function: int gsl_multiroot_fsolver_iterate (gsl_multiroot_fsolver * s)

 Function: int gsl_multiroot_fdfsolver_iterate (gsl_multiroot_fdfsolver * s)

These functions perform a single iteration of the solver s. If the
iteration encounters an unexpected problem then an error code will be
returned,
GSL_EBADFUNC

the iteration encountered a singular point where the function or its
derivative evaluated to
Inf
or NaN
.
GSL_ENOPROG

the iteration is not making any progress, preventing the algorithm from
continuing.
The solver maintains a current best estimate of the root at all times.
This information can be accessed with the following auxiliary functions,
 Function: gsl_vector * gsl_multiroot_fsolver_root (const gsl_multiroot_fsolver * s)

 Function: gsl_vector * gsl_multiroot_fdfsolver_root (const gsl_multiroot_fdfsolver * s)

These functions return the current estimate of the root for the solver s.
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