The model of asynchronous parallel nonlinear multisplitting method on shared memory system

Nonlinear multisplitting method is known as parallel iterative methods for solving a large-scale system of nonlinear equationsF(x)=0. We extend the idea of nonlinear multisplitting and consider a new model in which the iteration is executed asynchronously: Each processor calculate the solution of an individual nonlinear system belong to its nonlinear multisplitting and can update the global approximation residing in the shared memory at any time. A local convergence analysis of this model is presented. Finally, we give a numerical example which shows a ‘strange’ property that speedupS _p>p and efficiencyE _p>1.