Local convergence

Innumerical analysis,aniterative methodis calledlocally convergentif the successiveapproximationsproduced by the method are guaranteed toconvergeto a solution when the initial approximation is already close enough to the solution. Iterative methods fornonlinear equationsand their systems, such asNewton's methodare usually only locally convergent.

An iterative method that converges for an arbitrary initial approximation is calledglobally convergent.Iterative methods for systems oflinear equationsare usually globally convergent.