In
computational mathematics, an
iterative method is a mathematical procedure that generates a sequence of improving approximate solutions for a class of problems. A specific implementation of an iterative method, including the
termination criteria, is an
algorithm of the iterative method. An iterative method is called
convergent if the corresponding sequence converges for given initial approximations. A mathematically rigorous convergence analysis of an iterative method is usually performed; however,
heuristic-based iterative methods are also common. In the problems of
finding the root of an equation (or a solution of a system of equations), an iterative method uses an initial guess to generate successive
approximations to a solution.