In this paper,a two-step iteration method is established which can be viewed as a generalization of the existing modulus-based methods for vertical linear complementarity problems given by He and Vong(Appl.Math.Lett.1...In this paper,a two-step iteration method is established which can be viewed as a generalization of the existing modulus-based methods for vertical linear complementarity problems given by He and Vong(Appl.Math.Lett.134:108344,2022).The convergence analysis of the proposed method is established,which can improve the existing results.Numerical examples show that the proposed method is efficient with the two-step technique.展开更多
The mathematical formulation of the mixed-cell-height circuit legalization(MCHCL)problem can be expressed by a linear complementarity problem(LCP)with the system matrix being a block two-by-two saddle point matrix.Bas...The mathematical formulation of the mixed-cell-height circuit legalization(MCHCL)problem can be expressed by a linear complementarity problem(LCP)with the system matrix being a block two-by-two saddle point matrix.Based on the robust modulus-based matrix splitting(RMMS)iteration method and its two-step improvement(RTMMS)studied recently,the well-known Hermitian and skew-Hermitian splitting iteration method and the generalized successive overrelaxation iteration method for solving saddle point linear systems,two variants of robust two-step modulus-based matrix splitting(VRTMMS)iteration methods are proposed for solving the MCHCL problem.Convergence analyses of the proposed two iteration methods are studied in detail.Finally,five test problems are presented.Numerical results show that the proposed two VRTMMS iteration methods not only take full use of the sparse property of the circuit system but also speed up the computational efficiency of the existing RMMS and RTMMS iteration methods for solving the MCHCL problem.展开更多
In this paper,the modulus-based matrix splitting(MMS)iteration method is extended to solve the horizontal quasi-complementarity problem(HQCP),which is characterized by the presence of two system matrices and two nonli...In this paper,the modulus-based matrix splitting(MMS)iteration method is extended to solve the horizontal quasi-complementarity problem(HQCP),which is characterized by the presence of two system matrices and two nonlinear functions.Based on the specific matrix splitting of the system matrices,a series of MMS relaxation iteration methods are presented.Convergence analyses of the MMS iteration method are carefully studied when the system matrices are positive definite matrices and H_(+)-matrices,respectively.Finally,two numerical examples are given to illustrate the efficiency of the proposed MMS iteration methods.展开更多
Several preconditioners are proposed for improving the convergence rate of the iterative method derived from splitting. In this paper, the comparison theorem of preconditioned iterative method for regular splitting is...Several preconditioners are proposed for improving the convergence rate of the iterative method derived from splitting. In this paper, the comparison theorem of preconditioned iterative method for regular splitting is proved. And the convergence and comparison theorem for any preconditioner are indicated. This comparison theorem indicates the possibility of finding new preconditioner and splitting. The purpose of this paper is to show that the preconditioned iterative method yields a new splitting satisfying the regular or weak regular splitting. And new combination preconditioners are proposed. In order to denote the validity of the comparison theorem, some numerical examples are shown.展开更多
Kellogg gave a version of the Peaceman-Radford method. In this paper, we introduce a SSOR iteration method which uses Kellogg’s method. The new algorithm has some advantages over the traditional SSOR algorithm. A Cyc...Kellogg gave a version of the Peaceman-Radford method. In this paper, we introduce a SSOR iteration method which uses Kellogg’s method. The new algorithm has some advantages over the traditional SSOR algorithm. A Cyclic Reduction algorithm is introduced via a decoupling in Kellogg’s method.展开更多
We propose the modulus-based cascadic multigrid(MCMG)method and the modulus-based economical cascadic multigrid method for solving the quasi-variational inequalities problem.The modulus-based matrix splitting iterativ...We propose the modulus-based cascadic multigrid(MCMG)method and the modulus-based economical cascadic multigrid method for solving the quasi-variational inequalities problem.The modulus-based matrix splitting iterative method is adopted as a smoother,which can accelerate the convergence of the new methods.We also give the convergence analysis of these methods.Finally,some numerical experiments confirm the theoretical analysis and show that the new methods can achieve high efficiency and lower costs simultaneously.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
基金supported by the Scientific Computing Research Innovation Team of Guangdong Province(no.2021KCXTD052)the Science and Technology Development Fund,Macao SAR(no.0096/2022/A,0151/2022/A)+3 种基金University of Macao(no.MYRG2020-00035-FST,MYRG2022-00076-FST)the Guangdong Key Construction Discipline Research Capacity Enhancement Project(no.2022ZDJS049)Technology Planning Project of Shaoguan(no.210716094530390)the ScienceFoundation of Shaoguan University(no.SZ2020KJ01).
文摘In this paper,a two-step iteration method is established which can be viewed as a generalization of the existing modulus-based methods for vertical linear complementarity problems given by He and Vong(Appl.Math.Lett.134:108344,2022).The convergence analysis of the proposed method is established,which can improve the existing results.Numerical examples show that the proposed method is efficient with the two-step technique.
基金National Natural Science Foundation of China(No.11771225)the Qinglan Project of Jiangsu Province and the Science and Technology Project of Nantong City of China(No.JC2021198).
文摘The mathematical formulation of the mixed-cell-height circuit legalization(MCHCL)problem can be expressed by a linear complementarity problem(LCP)with the system matrix being a block two-by-two saddle point matrix.Based on the robust modulus-based matrix splitting(RMMS)iteration method and its two-step improvement(RTMMS)studied recently,the well-known Hermitian and skew-Hermitian splitting iteration method and the generalized successive overrelaxation iteration method for solving saddle point linear systems,two variants of robust two-step modulus-based matrix splitting(VRTMMS)iteration methods are proposed for solving the MCHCL problem.Convergence analyses of the proposed two iteration methods are studied in detail.Finally,five test problems are presented.Numerical results show that the proposed two VRTMMS iteration methods not only take full use of the sparse property of the circuit system but also speed up the computational efficiency of the existing RMMS and RTMMS iteration methods for solving the MCHCL problem.
基金supported by the National Natural Science Foundation of China(No.11771225)the Qinglan Project of Jiangsu Province of Chinathe Science and Technology Project of Nantong City of China(No.JC2021198).
文摘In this paper,the modulus-based matrix splitting(MMS)iteration method is extended to solve the horizontal quasi-complementarity problem(HQCP),which is characterized by the presence of two system matrices and two nonlinear functions.Based on the specific matrix splitting of the system matrices,a series of MMS relaxation iteration methods are presented.Convergence analyses of the MMS iteration method are carefully studied when the system matrices are positive definite matrices and H_(+)-matrices,respectively.Finally,two numerical examples are given to illustrate the efficiency of the proposed MMS iteration methods.
文摘Several preconditioners are proposed for improving the convergence rate of the iterative method derived from splitting. In this paper, the comparison theorem of preconditioned iterative method for regular splitting is proved. And the convergence and comparison theorem for any preconditioner are indicated. This comparison theorem indicates the possibility of finding new preconditioner and splitting. The purpose of this paper is to show that the preconditioned iterative method yields a new splitting satisfying the regular or weak regular splitting. And new combination preconditioners are proposed. In order to denote the validity of the comparison theorem, some numerical examples are shown.
文摘Kellogg gave a version of the Peaceman-Radford method. In this paper, we introduce a SSOR iteration method which uses Kellogg’s method. The new algorithm has some advantages over the traditional SSOR algorithm. A Cyclic Reduction algorithm is introduced via a decoupling in Kellogg’s method.
基金National Natural Science Foundation of China(12161027)Guangxi Natural Science Foundation,China(2020GXNSFAA159143)Science and Technology Project of Guangxi,China(AD23023002).
文摘We propose the modulus-based cascadic multigrid(MCMG)method and the modulus-based economical cascadic multigrid method for solving the quasi-variational inequalities problem.The modulus-based matrix splitting iterative method is adopted as a smoother,which can accelerate the convergence of the new methods.We also give the convergence analysis of these methods.Finally,some numerical experiments confirm the theoretical analysis and show that the new methods can achieve high efficiency and lower costs simultaneously.
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.
