Iteratívne

Iteratívne is a Slovak term describing processes, methods, or approaches that proceed through repeated cycles with the aim of improving a result or approaching a solution. The related noun is iterácia and the adjective form is iteratívny; the adverb is iteratívne. The concept is common in technical and scientific writing and emphasizes incremental refinement and approximation.

In mathematics and numerical analysis, iteratívne methods generate a sequence of approximations that ideally converges to an exact solution. Each step updates the current estimate according to a rule, and a stopping condition or convergence criterion determines when the process ends. The approach is well suited for large or complex problems where direct solutions are impractical, though convergence is not always guaranteed and performance can depend on the initial guess and the chosen update rule.

Common examples of iteratívne methods include fixed-point iteration, the Newton-Raphson method for root finding, and iterative linear solvers such as Jacobi and Gauss-Seidel. In optimization, iterative schemes like gradient descent refine candidate solutions by repeated improvement steps, often guided by a loss or objective function.

In software development and engineering, iterative development describes cycles of planning, implementation, testing, and evaluation that progressively refine a product. Each iteration yields a working increment and incorporates feedback, enabling more frequent reassessment of requirements and design compared with linear, one-pass approaches.

Overall, iteratívne emphasizes repeated refinement, gradual convergence toward a desired outcome, and the balancing of efficiency, accuracy, and practical constraints in technical work. See also: iterácia, konvergencia, iterácia v numerických metódach.