A(n) <u>iterative</u> procedure starts with an initial solution and uses it as a basis to calculate a series of solutions.
In computational mathematics, an iterative process is a mathematical procedure that produces improved approximate solutions to a class of problems from initial values, where the nth approximation is derived from the previous approximation. A specific implementation of an iterative process that includes termination criteria is the iterative process algorithm.
An iterative procedure is called convergent if the corresponding sequence converges to a given initial approximation. Mathematically rigorous convergence analysis of an iterative procedure is usually performed. However, iterative methods based on heuristics are also common.
By contrast, direct methods attempt to solve the problem through a finite set of operations. If there is no roundoff error, the direct method gives the exact solution. Iterative methods are often the only option for nonlinear equations. However, iterative methods are often useful in linear multivariate problems where direct methods are prohibitively expensive, even with the best computing power available.
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