In this paper, the asynchronous versions of classical iterative methods for solving linear systems of equations are considered. Sufficient conditions for convergence of asynchronous relaxed processes are given for H-m...In this paper, the asynchronous versions of classical iterative methods for solving linear systems of equations are considered. Sufficient conditions for convergence of asynchronous relaxed processes are given for H-matrix by which nor only the requirements of [3] on coefficient matrix are lowered, but also a larger region of convergence than that in [3] is obtained.展开更多
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
Presents a study of the numerical behaviors of the relaxed asynchronous multisplitting methods for linear complementarity problems by solving typical problems from practical applications on a real multiprocessor syste...Presents a study of the numerical behaviors of the relaxed asynchronous multisplitting methods for linear complementarity problems by solving typical problems from practical applications on a real multiprocessor system. Description of the tested problems and computing environment used in the computations; Description of the asynchronous multisplitting unsymmetric accelerated overrelaxation method; Discussion of results.展开更多
In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an a...In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an approach based on a non-converging state-value function that fluctuates（increases and decreases） between states of the dynamic process.We prove that it is possible to represent that function in a recursive format using a one-step-ahead fixed-optimal policy.Then,we provide an analytical formula for the numerical realization of the fixed local-optimal strategy.We also present a second approach based on linear programming,to solve the same problem,that implement the c-variable method for making the problem computationally tractable.At the end,we show that these two approaches are related：after a finite number of iterations our proposed approach converges to same result as the linear programming method.We also present a non-traditional approach for ergodicity verification.The validity of the proposed methods is successfully demonstrated theoretically and,by simulated credit-card marketing experiments computing the customer lifetime value for both an optimization and a game theory approach.展开更多
文摘In this paper, the asynchronous versions of classical iterative methods for solving linear systems of equations are considered. Sufficient conditions for convergence of asynchronous relaxed processes are given for H-matrix by which nor only the requirements of [3] on coefficient matrix are lowered, but also a larger region of convergence than that in [3] is obtained.
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.
基金the Special Funds for Major State Basic Research Projects G1999032803Supported by the National Natural Science Foundation of China (19601036).
文摘Presents a study of the numerical behaviors of the relaxed asynchronous multisplitting methods for linear complementarity problems by solving typical problems from practical applications on a real multiprocessor system. Description of the tested problems and computing environment used in the computations; Description of the asynchronous multisplitting unsymmetric accelerated overrelaxation method; Discussion of results.
文摘In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an approach based on a non-converging state-value function that fluctuates（increases and decreases） between states of the dynamic process.We prove that it is possible to represent that function in a recursive format using a one-step-ahead fixed-optimal policy.Then,we provide an analytical formula for the numerical realization of the fixed local-optimal strategy.We also present a second approach based on linear programming,to solve the same problem,that implement the c-variable method for making the problem computationally tractable.At the end,we show that these two approaches are related：after a finite number of iterations our proposed approach converges to same result as the linear programming method.We also present a non-traditional approach for ergodicity verification.The validity of the proposed methods is successfully demonstrated theoretically and,by simulated credit-card marketing experiments computing the customer lifetime value for both an optimization and a game theory approach.
