iterativas

Iterativas is the plural form of iterativo in Spanish and Portuguese, used to describe processes, methods, or designs that rely on iteration. In this sense, an iterative approach generates successive approximations to a desired result, improving upon previous estimates rather than attempting a final solution in a single step.

In mathematics, numerical computing, and computer science, iterative methods are procedures that produce a sequence x0, x1, x2, ... intended to converge to a solution x*. Convergence depends on the mathematical properties of the problem and on stopping criteria.

Common examples include fixed-point iteration, Newton-Raphson, and the Jacobi and Gauss-Seidel methods for solving linear systems; gradient descent and related optimization techniques; and expectation-maximization for parameter estimation in probabilistic models. In image processing and scientific computing, iterative refinement and deconvolution methods are widely used.

Iterative development is a software engineering approach in which requirements and solutions evolve through collaboration and incremental releases, often associated with agile methodologies. This approach emphasizes learning from each cycle, adjusting plans, and delivering usable increments rather than a single, fully specified product.

Advantages of iterative methods and processes include flexibility, adaptability to changing requirements, and the ability to tackle complex problems piece by piece. Limitations include the possibility of non-convergence, dependence on initial conditions, and the need for appropriate stopping criteria, tolerance levels, and performance monitoring.

In practice, practitioners choose initial guesses, convergence tests, and resource constraints to balance accuracy and computation time. Iterativas thus appear across domains such as numerical analysis, optimization, computer graphics, control systems, and data analysis.