Iterativo

Iterativo is an adjective used in several Romance languages to describe a process carried out in iterations or through successive refinements. In Italian, Spanish, and Portuguese, it translates roughly as “iterative” or “repetitive.” The term derives from the Latin iterare, to repeat, and iteratio, a repetition.

In mathematics and computer science, iterative methods generate a sequence of improving approximations to a solution. Examples include fixed-point iteration, and methods for solving linear systems such as Jacobi and Gauss-Seidel, as well as root-finding approaches like Newton-Raphson. These methods require a stopping criterion, such as a tolerance for the difference between successive approximations or a maximum number of iterations. Convergence depends on problem properties and the choice of starting point or parameters.

In software development, iterative refers to cycles of planning, design, implementation, and evaluation that produce incremental improvements. Iterative development emphasizes delivering working software in small increments, frequent feedback, and risk reduction, often contrasting with traditional linear models. Agile methodologies, including Scrum and XP, organize work into short iterations or sprints to maximize adaptability.

In design and research, iterative design or prototyping involves creating rough versions, testing them with users or stakeholders, and refining based on feedback. This approach aims to enhance usability, performance, and relevance while reducing costly changes later in the process.

Iterative approaches also appear in optimization, control systems, and simulations, where systems are repeatedly updated toward an established target or criterion. See also iteration and refinement.