Iterando

Iterando is the gerund form of the verb iterar in Spanish and Portuguese, meaning to perform iterations or to repeat steps in order to refine results. As a linguistic form, iterando describes ongoing action in processes that are repeated with the goal of improvement or convergence. The term derives from Latin iteratio, iteration.

In mathematics and computer science, iteration refers to the repeated application of a function or operation. Iterative methods generate successive approximations to a solution, often governed by convergence criteria such as error thresholds. Examples include fixed-point iteration, Newton-Raphson methods in their iterative form, and iterative optimization algorithms like gradient descent when closed-form solutions are not available. Iteration contrasts with recursion or direct (analytic) solutions.

In software development and product design, iteration denotes a time-boxed cycle in which a working version of a product is developed, tested, and evaluated before the next cycle. This approach is central to agile methodologies, where each iteration yields incremental improvements and informs subsequent work. Iterative development emphasizes feedback, learning, and refinement rather than delivering a single final product at once.

The term is commonly used across technical and general contexts to describe repetitive processes aimed at improving accuracy, performance, or user experience. See also iteration, iteración, and iterar for related concepts.