In this paper we describe a multi-grid algorithm for mixed problems with penalty by the linear finite element approximation. It is proved that the convergence rate of the algorithm is bound ed away from 1 independentl...In this paper we describe a multi-grid algorithm for mixed problems with penalty by the linear finite element approximation. It is proved that the convergence rate of the algorithm is bound ed away from 1 independently of the meshsize. For convenience, we only discuss Jacobi relaxation as smoothing operator in detail.展开更多
In this paper, we consider the low rank approximation solution of a generalized Lya- punov equation which arises in the bilinear model reduction. By using the variation prin- ciple, the low rank approximation solution...In this paper, we consider the low rank approximation solution of a generalized Lya- punov equation which arises in the bilinear model reduction. By using the variation prin- ciple, the low rank approximation solution problem is transformed into an unconstrained optimization problem, and then we use the nonlinear conjugate gradient method with ex- act line search to solve the equivalent unconstrained optimization problem. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed methods.展开更多
Using a bounding technique, we prove that the fluid model of generalized Jackson network （GJN） with vacations is the same as a GJN without vacations, which means that vacation mechanism does not affect the dynamic p...Using a bounding technique, we prove that the fluid model of generalized Jackson network （GJN） with vacations is the same as a GJN without vacations, which means that vacation mechanism does not affect the dynamic performance of GJN under fluid approximation. Furthermore, in order to present the impact of vacation on the performance of GJN, we show that exponential rate of convergence for fluid approximation only holds for large N, which is different from a GJN without vacations. The results on fluid approximation and convergence fate are embodied by the queue length, workload, and busy time processes.展开更多
In this paper,making use of upper and lower solutions,we first prove the existence of the solu tion for integral differential equation of Volterra type.Then applying the theory of differential in equalities obtained,u...In this paper,making use of upper and lower solutions,we first prove the existence of the solu tion for integral differential equation of Volterra type.Then applying the theory of differential in equalities obtained,under the appropriate assumptions,by constructing the special function of upper and lower solutions,we demonstrate the existence of the solution for singularly preturbed integral differential equation of Volterra type,and give the uniformly valid approximate estimation.展开更多
基金This work was supported by China State Major Key Project for Basic Researches
文摘In this paper we describe a multi-grid algorithm for mixed problems with penalty by the linear finite element approximation. It is proved that the convergence rate of the algorithm is bound ed away from 1 independently of the meshsize. For convenience, we only discuss Jacobi relaxation as smoothing operator in detail.
文摘In this paper, we consider the low rank approximation solution of a generalized Lya- punov equation which arises in the bilinear model reduction. By using the variation prin- ciple, the low rank approximation solution problem is transformed into an unconstrained optimization problem, and then we use the nonlinear conjugate gradient method with ex- act line search to solve the equivalent unconstrained optimization problem. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed methods.
文摘Using a bounding technique, we prove that the fluid model of generalized Jackson network （GJN） with vacations is the same as a GJN without vacations, which means that vacation mechanism does not affect the dynamic performance of GJN under fluid approximation. Furthermore, in order to present the impact of vacation on the performance of GJN, we show that exponential rate of convergence for fluid approximation only holds for large N, which is different from a GJN without vacations. The results on fluid approximation and convergence fate are embodied by the queue length, workload, and busy time processes.
文摘In this paper,making use of upper and lower solutions,we first prove the existence of the solu tion for integral differential equation of Volterra type.Then applying the theory of differential in equalities obtained,under the appropriate assumptions,by constructing the special function of upper and lower solutions,we demonstrate the existence of the solution for singularly preturbed integral differential equation of Volterra type,and give the uniformly valid approximate estimation.
