Subiteration

Subiteration refers to a process where a smaller, often simpler, iterative procedure is performed within the steps of a larger, outer iterative procedure. This nested structure is common in various computational and mathematical contexts. For example, in optimization algorithms, a subiteration might be used to find a local minimum or a specific parameter value within each major step of the overall optimization process. This inner loop refines a solution before the outer loop progresses to the next stage.

In numerical methods, subiteration can be employed when solving complex equations. A common scenario is the use of iterative solvers for systems of linear equations, where each iteration of an outer solver might involve multiple iterations of an inner solver to achieve a desired level of accuracy for a particular component or approximation. This allows for a more controlled and precise convergence towards the final solution.

The purpose of subiteration is typically to improve accuracy, stability, or computational efficiency. By breaking down a complex problem into smaller, manageable iterative steps, it can be easier to control the convergence and ensure that the overall process reaches a satisfactory outcome. The number of subiterations can be a parameter that is tuned to balance computational cost with the required precision.