ABSTRACT
In this chapter, we are interested in parallel synchronous iterative algorithms for linear and nonlinear systems. Convergence results of the synchronous versions and their implementations are detailed. We will concentrate on so-calledmultisplitting algorithms and their coupling
with the Newton method. Multisplitting algorithms include the discrete analogues of Schwarz multi-subdomain methods and hence are very suitable for distributed computing on distant heterogeneous clusters. They are particularly well suited for physical and natural problems modeled by elliptic systems and discretized by finite difference methods with natural ordering. The parallel versions of minimization like the methods exposed in Chap-
ter 2 are not detailed in this chapter but it should be mentioned that, thanks to the multisplitting approach and under suitable assumptions on the splittings, these methods can be used as inner iterations of two-stagemultisplitting algorithms.
