Newton additive and multiplicative Schwarz iterative methods

Daniel B. Szyld^¶Department of Mathematics, Temple University, Philadelphia, PA 19122, USA ^{Convergence properties are presented for Newton additive andmultiplicative Schwarz (AS and MS) iterative methods for thesolution of nonlinear systems in several variables. These methodsconsist of approximate solutions of the linear Newton step usingeither AS or MS iterations, where overlap between subdomainscan be used. Restricted versions of these methods are also considered.These Schwarz methods can also be used to precondition a Krylovsubspace method for the solution of the linear Newton steps.Numerical experiments on parallel computers are presented, indicatingthe effectiveness of these methods.}