Iter (plural: itera) is a Latin word meaning ‘journey’ or ‘way’. In the mathematical and physical sciences, it is often used to denote a sequence of repeated operations or events.
The term is also used in computer science, particularly in the area of algorithms, where an iterative algorithm is one that performs a finite number of steps in order to achieve a desired result. A common type of iterative algorithm is the loop, which repeats a set of instructions until some condition is met.
Iterative methods are often used when no closed-form solution exists for the problem at hand. That is, there does not exist a formula that can be used to directly compute the desired result. In such cases, an iterative approach may be the only way to obtain a solution.
One example of an iterative method is Newton’s Method for finding roots of equations. This method starts with an initial guess for the root and then uses successive approximations to improve upon this guess until the desired accuracy is achieved. Another example is the bisection method for finding roots, which repeatedly bisects an interval containing the root and checks whether the midpoint of each subinterval lies above or below the root before narrowing down on its location.