Most numerical root-finding methods are iterative methods, producing a sequence of numbers that ideally converges towards a root as a limit. They require one or more initial guesses of the root as starting values, then each iteration of the algorithm produces a successively more accurate approximation to the root. Since the iteration must be stopped at some point, these methods produce an approximation to the root, not an exact solution. Many methods compute subsequent values by evaluating an auxiliary function on the preceding values. The limit is thus a fixed point of the auxiliary function, which is chosen for having the roots of the original equation as fixed points and for converging rapidly to these fixed points.
Most numerical root-finding methods are iterative methods producing a sequence of numbers that ideally converges towards a root as a limit They require one or more initial guesses of the root as starting values, then each iteration of the algorithm produces a successively more accurate approximation to the root. Since the iteration must be stopped at some point, these methods produce an approximation to the root not an exact solution. Many methods compute subsequent values by evaluating a,n auxiliary function on the prece.ding values. The limit is thus a fixed point of the auxiliary function, which is chosen for having the roots of the original equation as fixed points a,nd for converging rapidly to these fixed points.