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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.

int gsl_root_fsolver_iterate (gsl_root_fsolver * s) Function
int gsl_root_fdfsolver_iterate (gsl_root_fdfsolver * s) Function
These functions perform a single iteration of the solver s. If the iteration encounters an unexpected problem then an error code will be returned,
the iteration encountered a singular point where the function or its derivative evaluated to Inf or NaN.
the derivative of the function vanished at the iteration point, preventing the algorithm from continuing without a division by zero.

The solver maintains a current best estimate of the root at all times. The bracketing solvers also keep track of the current best interval bounding the root. This information can be accessed with the following auxiliary functions,

double gsl_root_fsolver_root (const gsl_root_fsolver * s) Function
double gsl_root_fdfsolver_root (const gsl_root_fdfsolver * s) Function
These functions return the current estimate of the root for the solver s.

double gsl_root_fsolver_x_lower (const gsl_root_fsolver * s) Function
double gsl_root_fsolver_x_upper (const gsl_root_fsolver * s) Function
These functions return the current bracketing interval for the solver s.