Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate o...Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate of this method is investigated.展开更多
In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient proje...In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.展开更多
Recently,the projected Jacobi(PJ)and projected Gauss-Seidel(PGS)iteration methods have been studied for solving the horizontal linear complementarity problems(HLCPs).To further improve the convergence rates of the PJ ...Recently,the projected Jacobi(PJ)and projected Gauss-Seidel(PGS)iteration methods have been studied for solving the horizontal linear complementarity problems(HLCPs).To further improve the convergence rates of the PJ and PGS iteration methods,by using the successive overrelaxation(SOR)matrix splitting technique,a projected SOR iteration method is introduced in this paper to solve the HLCP.Convergence analyses are carefully studied when the system matrices are strictly diagonally dominant and irreducibly diagonally dominant.The newly obtained convergence results greatly extend the current convergence theory.Finally,two numerical examples are given to show the effectiveness of the proposed PSOR iteration method and its advantages over the recently proposed PJ and PGS iteration methods.展开更多
Asynchronous parallel multisplitting relaxation methods for solving large sparse linear complementarity problems are presented, and their convergence is proved when the system matrices are H-matrices having positive d...Asynchronous parallel multisplitting relaxation methods for solving large sparse linear complementarity problems are presented, and their convergence is proved when the system matrices are H-matrices having positive diagonal elements. Moreover, block and multi-parameter variants of the new methods, together with their convergence properties, are investigated in detail. Numerical results show that these new methods can achieve high parallel efficiency for solving the large sparse linear complementarity problems on multiprocessor systems.展开更多
Focuses on a study which presented a parallel chaotic multisplitting method for solving the large sparse linear complementarity problem. Preliminaries of the study; Equations of the parallel chaotic multisplitting met...Focuses on a study which presented a parallel chaotic multisplitting method for solving the large sparse linear complementarity problem. Preliminaries of the study; Equations of the parallel chaotic multisplitting method; Information on the convergence theories; Details on the parallel chaotic multisplitting relaxation methods.展开更多
Presents a class of relaxed asynchronous parallel multisplitting iterative methods for solving the linear complementarity problem on multiprocessor systems. Establishment of the methods; Convergence theories; Numerica...Presents a class of relaxed asynchronous parallel multisplitting iterative methods for solving the linear complementarity problem on multiprocessor systems. Establishment of the methods; Convergence theories; Numerical results.展开更多
文摘Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate of this method is investigated.
文摘In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.
基金National Natural Science Foundation of China(No.11771225)Qinglan Project of Jiangsu Province of China.
文摘Recently,the projected Jacobi(PJ)and projected Gauss-Seidel(PGS)iteration methods have been studied for solving the horizontal linear complementarity problems(HLCPs).To further improve the convergence rates of the PJ and PGS iteration methods,by using the successive overrelaxation(SOR)matrix splitting technique,a projected SOR iteration method is introduced in this paper to solve the HLCP.Convergence analyses are carefully studied when the system matrices are strictly diagonally dominant and irreducibly diagonally dominant.The newly obtained convergence results greatly extend the current convergence theory.Finally,two numerical examples are given to show the effectiveness of the proposed PSOR iteration method and its advantages over the recently proposed PJ and PGS iteration methods.
基金Subsidized by The Special Funds For Major State Basic Research Projects G1999032803.
文摘Asynchronous parallel multisplitting relaxation methods for solving large sparse linear complementarity problems are presented, and their convergence is proved when the system matrices are H-matrices having positive diagonal elements. Moreover, block and multi-parameter variants of the new methods, together with their convergence properties, are investigated in detail. Numerical results show that these new methods can achieve high parallel efficiency for solving the large sparse linear complementarity problems on multiprocessor systems.
基金the National Natural Science Foundation of China (19601036) and Subsidized by the SpecialFunds for Major State Basic Research
文摘Focuses on a study which presented a parallel chaotic multisplitting method for solving the large sparse linear complementarity problem. Preliminaries of the study; Equations of the parallel chaotic multisplitting method; Information on the convergence theories; Details on the parallel chaotic multisplitting relaxation methods.
基金The Special Funds For Major State Basic Research Project G1999032803.
文摘Presents a class of relaxed asynchronous parallel multisplitting iterative methods for solving the linear complementarity problem on multiprocessor systems. Establishment of the methods; Convergence theories; Numerical results.
