Pysäytysehto

Pysäytysehto, Finnish for stopping condition, refers to a criterion that determines when to terminate an iterative computation, algorithm, or process. It is used across mathematics, computer science, and data analysis to ensure termination and control resource consumption. A stopping condition can be explicit (a fixed number of iterations or time limit) or based on the state of the computation (tolerance-based, convergence criteria, or stagnation).

Common forms include absolute tolerance |f(x_n)| <= tol, relative tolerance |x_{n+1}-x_n|/|x_n| <= tol, or a combination. In optimization and numerical methods, typical criteria involve the magnitude of the function or the update step. In search and pathfinding, stopping occurs when the goal is removed from the frontier or when path cost meets threshold. In machine learning, early stopping monitors performance on a hold-out validation set and uses patience to prevent overfitting.

Choosing a pysäytysehto affects accuracy and efficiency; too strict may cause unnecessary computation or non-convergence; too loose may yield imprecise results. It often requires problem-specific tuning, normalization of scales, and sometimes multiple criteria with a logical conjunction or disjunction.

Examples: Newton-Raphson method stops when |f(x_n)| < tol; bisection method stops when interval length < tol; Dijkstra's algorithm halts when the target node is dequeued; gradient descent stops when gradient norm is below tol; early stopping in neural network training halts when validation loss fails to improve for a number of epochs (patience).