Iterativ

Iterativ is an adjective used to describe processes or methods that achieve results through repeated cycles, with each cycle refining the outcome. The term emphasizes refinement through feedback rather than a single, one-shot action.

In mathematics and numerical analysis, iterative methods build a sequence intended to converge to a solution. A step computes x_{k+1} from x_k; convergence depends on properties of the function or operator and is assessed by stopping criteria such as tolerances or residuals. Common examples include fixed-point iteration, the Gauss-Seidel and Jacobi methods for linear systems, and iterative optimization algorithms such as gradient descent and Newton’s method when used in an iterative manner.

In computer science and software development, iterative approaches organize work in repeated cycles, enabling incremental improvement and frequent feedback. Agile development, iterative design, and related practices apply these cycles to activities such as requirements gathering, prototyping, testing, and refinement rather than following a single linear plan.

The term derives from Latin iterare “to repeat,” and is used across disciplines to distinguish cyclical refinement from non-iterative or one-pass methods. Related concepts include recursion (a method that calls itself) and convergence (the attainment of a stable solution).