Nonlinear multisplitting method is known as parallel iterative methods for solving a large-scale system of nonlinear equations F(x) = 0. We extend the idea of nonlinear multisplitting and consider a new model ill whic...Nonlinear multisplitting method is known as parallel iterative methods for solving a large-scale system of nonlinear equations F(x) = 0. We extend the idea of nonlinear multisplitting and consider a new model ill 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 uumerical example which shows a 'strange' property that speedup Sp > p and efficiency Ep > 1.展开更多
This paper proposes a class of asynchronous block iterative methods for solving large scale nonlinear equations F(x)=0 and proves local convergence. This method splits F into p blocks, then does the asynch...This paper proposes a class of asynchronous block iterative methods for solving large scale nonlinear equations F(x)=0 and proves local convergence. This method splits F into p blocks, then does the asynchronous parallel iteration on the p multiprocessor with shared memory. Because each processor need only solve equations with a low dimension and there is no synchronous waiting time, the parallel efficiency can be increased. Finally, we give the results of the numerical test of three kinds of Newton like asynchronous block iteration methods which run well on a multiprocessor system. These results show that the parallel efficiency is very high.展开更多
文摘Nonlinear multisplitting method is known as parallel iterative methods for solving a large-scale system of nonlinear equations F(x) = 0. We extend the idea of nonlinear multisplitting and consider a new model ill 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 uumerical example which shows a 'strange' property that speedup Sp > p and efficiency Ep > 1.
基金Supported by the National Natural Scie-nce Foundation of China
文摘This paper proposes a class of asynchronous block iterative methods for solving large scale nonlinear equations F(x)=0 and proves local convergence. This method splits F into p blocks, then does the asynchronous parallel iteration on the p multiprocessor with shared memory. Because each processor need only solve equations with a low dimension and there is no synchronous waiting time, the parallel efficiency can be increased. Finally, we give the results of the numerical test of three kinds of Newton like asynchronous block iteration methods which run well on a multiprocessor system. These results show that the parallel efficiency is very high.
