# Iterative Algorithm

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An Iterative Algorithm is an algorithm strategy that iterates between two or more algorithm steps.

## References

### 2015

• (Wikipedia, 2015) ⇒ http://wikipedia.org/wiki/Iteration#Computing Retrieved:2015-7-9.
• Iteration in computing is the repetition of a block of statements within a computer program. It can be used both as a general term, synonymous with repetition, and to describe a specific form of repetition with a mutable state. Confusingly, it may also refer to any repetition stated using an explicit repetition structure, regardless of mutability.

### 2012

• http://en.wikipedia.org/wiki/Iterative_method
• QUOTE: 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. In contrast, direct methods attempt to solve the problem by a finite sequence of operations. In the absence of rounding errors, direct methods would deliver an exact solution (like solving a linear system of equations Ax = b by Gaussian elimination). Iterative methods are often the only choice for nonlinear equations. However, iterative methods are often useful even for linear problems involving a large number of variables (sometimes of the order of millions), where direct methods would be prohibitively expensive (and in some cases impossible) even with the best available computing power.