Relaxation (iterative method)

In numerical mathematics, relaxation methods are iterative methods for solving systems of equations, including nonlinear systems.When φ is a smooth real-valued function on the real numbers, its second derivative can be approximated by:While the method converges under general conditions, it typically makes slower progress than competing methods. Nonetheless, the study of relaxation methods remains a core part of linear algebra, because the transformations of relaxation theory provide excellent preconditioners for new methods. Indeed, the choice of preconditioner is often more important than the choice of iterative method.