In this paper, we consider preconditioners for generalized saddle point systems with a nonsymmetric coefficient matrix. A constraint preconditioner for this systems is constructed, and some spectral properties of the ...In this paper, we consider preconditioners for generalized saddle point systems with a nonsymmetric coefficient matrix. A constraint preconditioner for this systems is constructed, and some spectral properties of the preconditioned matrix are given. Our results extend the corresponding ones in [3] and [4].展开更多
针对一类具结构的非对称线性方程组提出了一类子结构预处理子,该预处理子只保留了约束条件的一半项.研究表明,预处理矩阵只有三个离散的特征值.为了避免计算Schur补的逆,还给出了正则化的子结构预处理子,同样对预处理矩阵进行了谱分析....针对一类具结构的非对称线性方程组提出了一类子结构预处理子,该预处理子只保留了约束条件的一半项.研究表明,预处理矩阵只有三个离散的特征值.为了避免计算Schur补的逆,还给出了正则化的子结构预处理子,同样对预处理矩阵进行了谱分析.这些结果将Zhou和Niu(Zhou J T,Niu Q.Substructure preconditioners for a class of structuredlinear systems of equations.Math.Comput.Model.,2010,52:1547-1553)的结果推广到非对称结构线性方程组.数值算例验证了提出的子结构预处理子的有效性.展开更多
Linear precoding methods such as zero-forcing(ZF)are near optimal for downlink massive multi-user multiple input multiple output(MIMO)systems due to their asymptotic channel property.However,as the number of users inc...Linear precoding methods such as zero-forcing(ZF)are near optimal for downlink massive multi-user multiple input multiple output(MIMO)systems due to their asymptotic channel property.However,as the number of users increases,the computational complexity of obtaining the inverse matrix of the gram matrix increases.Forsolving the computational complexity problem,this paper proposes an improved Jacobi(JC)-based precoder to improve error performance of the conventional JC in the downlink massive MIMO systems.The conventional JC was studied for solving the high computational complexity of the ZF algorithm and was able to achieve parallel implementation.However,the conventional JC has poor error performance when the number of users increases,which means that the diagonal dominance component of the gram matrix is reduced.In this paper,the preconditioning method is proposed to improve the error performance.Before executing the JC,the condition number of the linear equation and spectrum radius of the iteration matrix are reduced by multiplying the preconditioning matrix of the linear equation.To further reduce the condition number of the linear equation,this paper proposes a polynomial expansion precondition matrix that supplements diagonal components.The results show that the proposed method provides better performance than other iterative methods and has similar performance to the ZF.展开更多
A framework for parallel algebraic multilevel preconditioning methods presented for solving large sparse systems of linear equstions with symmetric positive definite coefficient matrices,which arise in suitable finite...A framework for parallel algebraic multilevel preconditioning methods presented for solving large sparse systems of linear equstions with symmetric positive definite coefficient matrices,which arise in suitable finite element discretizations of many second-order self-adjoint elliptic boundary value problems. This framework not only covers all known parallel algebraic multilevel preconditioning methods, but also yields new ones. It is shown that all preconditioners within this framework have optimal orders of complexities for problems in two-dimensional(2-D) and three-dimensional (3-D) problem domains, and their relative condition numbers are bounded uniformly with respect to the numbers of both levels and nodes.展开更多
A framework for algebraic multilevel preconditioning methods is presented for solving largesparse systems of linear equations with symmetric positive definite coefficient matrices, whicharise in the discretization of ...A framework for algebraic multilevel preconditioning methods is presented for solving largesparse systems of linear equations with symmetric positive definite coefficient matrices, whicharise in the discretization of second order elliptic boundary value problems by the finite elementmethod. This framework covers not only all known algebraic multilevel preconditioning methods,but yields also new ones. It is shown that all preconditioners within this framework have optimalorders of complexities for problems in two-dimensional (2-D) and three-dimensional(3-D) problemdomains, and their relative condition numbers are bounded uniformly with respect to the numbersof both the levels and the nodes.展开更多
基金Supported by the Natural Science Foundation of Guangdong Province (06025061, 91510224000002)the National Natural Science Foundation of China (10971075, 10671077)the State Key Laboratory of Scientific and Engineering Computing
文摘In this paper, we consider preconditioners for generalized saddle point systems with a nonsymmetric coefficient matrix. A constraint preconditioner for this systems is constructed, and some spectral properties of the preconditioned matrix are given. Our results extend the corresponding ones in [3] and [4].
基金supported by the National Natural Science Pre-Research Foundation(SDY2011B01)the College Postgraduate Research and Innovation Project of Jiangsu Province(CX10B-029Z)the Nominated Excellent Thesis for PHD Candidates Program of Soochow University(23320957)
文摘针对一类具结构的非对称线性方程组提出了一类子结构预处理子,该预处理子只保留了约束条件的一半项.研究表明,预处理矩阵只有三个离散的特征值.为了避免计算Schur补的逆,还给出了正则化的子结构预处理子,同样对预处理矩阵进行了谱分析.这些结果将Zhou和Niu(Zhou J T,Niu Q.Substructure preconditioners for a class of structuredlinear systems of equations.Math.Comput.Model.,2010,52:1547-1553)的结果推广到非对称结构线性方程组.数值算例验证了提出的子结构预处理子的有效性.
基金supported by the MSIT(Ministry of Science and ICT),Korea,under the ITRC(Information Technology Research Center)support program(IITP-2019-2018-0-01423)supervised by the IITP(Institute for Information&communications Technology Promotion)+1 种基金supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(2020R1A6A1A03038540).
文摘Linear precoding methods such as zero-forcing(ZF)are near optimal for downlink massive multi-user multiple input multiple output(MIMO)systems due to their asymptotic channel property.However,as the number of users increases,the computational complexity of obtaining the inverse matrix of the gram matrix increases.Forsolving the computational complexity problem,this paper proposes an improved Jacobi(JC)-based precoder to improve error performance of the conventional JC in the downlink massive MIMO systems.The conventional JC was studied for solving the high computational complexity of the ZF algorithm and was able to achieve parallel implementation.However,the conventional JC has poor error performance when the number of users increases,which means that the diagonal dominance component of the gram matrix is reduced.In this paper,the preconditioning method is proposed to improve the error performance.Before executing the JC,the condition number of the linear equation and spectrum radius of the iteration matrix are reduced by multiplying the preconditioning matrix of the linear equation.To further reduce the condition number of the linear equation,this paper proposes a polynomial expansion precondition matrix that supplements diagonal components.The results show that the proposed method provides better performance than other iterative methods and has similar performance to the ZF.
文摘A framework for parallel algebraic multilevel preconditioning methods presented for solving large sparse systems of linear equstions with symmetric positive definite coefficient matrices,which arise in suitable finite element discretizations of many second-order self-adjoint elliptic boundary value problems. This framework not only covers all known parallel algebraic multilevel preconditioning methods, but also yields new ones. It is shown that all preconditioners within this framework have optimal orders of complexities for problems in two-dimensional(2-D) and three-dimensional (3-D) problem domains, and their relative condition numbers are bounded uniformly with respect to the numbers of both levels and nodes.
文摘A framework for algebraic multilevel preconditioning methods is presented for solving largesparse systems of linear equations with symmetric positive definite coefficient matrices, whicharise in the discretization of second order elliptic boundary value problems by the finite elementmethod. This framework covers not only all known algebraic multilevel preconditioning methods,but yields also new ones. It is shown that all preconditioners within this framework have optimalorders of complexities for problems in two-dimensional (2-D) and three-dimensional(3-D) problemdomains, and their relative condition numbers are bounded uniformly with respect to the numbersof both the levels and the nodes.
