Endofiteration

Endofiteration is a term used to describe the boundary that marks the conclusion of one cycle in an iterative process. It denotes the transition to the next iteration, or to termination if the stopping condition has been met. The concept is applicable across programming, mathematics, and numerical methods where processes repeatedly refine a state or estimate.

In programming, a loop such as a for or while executes its body and then evaluates a condition to decide whether to repeat. The end of iteration occurs after the loop body runs and before the next cycle begins. Some constructs, like do-while or repeat-until loops, explicitly define this boundary at the point where control goes back to the loop's condition check.

In numerical and algorithmic contexts, each iteration applies an update rule to produce a new estimate or state. Common tasks at the end of an iteration include computing an error measure or residual, updating auxiliary variables, and deciding whether to continue. The end-of-iteration phase is frequently when convergence is checked, for example by comparing the change in successive estimates to a tolerance or by assessing the residual norm.

Termination conditions govern when iterations stop. These can be a predetermined maximum number of iterations, satisfaction of a convergence criterion, or an external interruption. Proper handling of the end of iteration is important for performance, numerical stability, and correct control flow in both sequential and parallel implementations.

See also: loop, iteration, stopping criterion, convergence, fixed-point iteration, gradient descent, Jacobi method.