The Hermitian and skew-Hermitian splitting （HSS） method is an unconditionally convergent iteration method for solving large sparse non-Hermitian positive definite system of linear equations. By making use of the HSS...The Hermitian and skew-Hermitian splitting （HSS） method is an unconditionally convergent iteration method for solving large sparse non-Hermitian positive definite system of linear equations. By making use of the HSS iteration as the inner solver for the Newton method, we establish a class of Newton-HSS methods for solving large sparse systems of nonlinear equations with positive definite Jacobian matrices at the solution points. For this class of inexact Newton methods, two types of local convergence theorems are proved under proper conditions, and numerical results are given to examine their feasibility and effectiveness. In addition, the advantages of the Newton-HSS methods over the Newton-USOR, the Newton-GMRES and the Newton-GCG methods are shown through solving systems of nonlinear equations arising from the finite difference discretization of a two-dimensional convection-diffusion equation perturbed by a nonlinear term. The numerical implemen- tations also show that as preconditioners for the Newton-GMRES and the Newton-GCG methods the HSS iteration outperforms the USOR iteration in both computing time and iteration step.展开更多
白中治等提出了解非埃尔米特正定线性方程组的埃尔米特和反埃尔米特分裂(HSS)迭代方法(Bai Z Z,Golub G H,Ng M K.Hermitian and skew-Hermitian splitting methodsfor non-Hermitian positive definite linear systems.SIAM J.Matrix A...白中治等提出了解非埃尔米特正定线性方程组的埃尔米特和反埃尔米特分裂(HSS)迭代方法(Bai Z Z,Golub G H,Ng M K.Hermitian and skew-Hermitian splitting methodsfor non-Hermitian positive definite linear systems.SIAM J.Matrix Anal.Appl.,2003,24:603-626).本文精确地估计了用HSS迭代方法求解广义鞍点问题时在加权2-范数和2-范数下的收缩因子.在实际的计算中,正是这些收缩因子而不是迭代矩阵的谱半径,本质上控制着HSS迭代方法的实际收敛速度.根据文中的分析,求解广义鞍点问题的HSS迭代方法的收缩因子在加权2-范数下等于1,在2-范数下它会大于等于1,而在某种适当选取的范数之下,它则会小于1.最后,用数值算例说明了理论结果的正确性.展开更多
提出了求解广义Lyapunov方程的HSS(Hermitian and skew-Hermitian splitting)迭代法,分析了该方法的收敛性,给出了收敛因子的上界.为了降低HSS迭代法的计算量,提出了求解广义Lyapunov方程的非精确HSS迭代法,并分析其收敛性.数值结果表明...提出了求解广义Lyapunov方程的HSS(Hermitian and skew-Hermitian splitting)迭代法,分析了该方法的收敛性,给出了收敛因子的上界.为了降低HSS迭代法的计算量,提出了求解广义Lyapunov方程的非精确HSS迭代法,并分析其收敛性.数值结果表明,求解广义Lyapunov方程的HSS迭代法及非精确HSS迭代法是有效的.展开更多
Based on the two-dimensional three-temperature （2D3T） radiation diffusion equations and its discrete system, using the block diagonal structure of the three-temperature matrix, the reordering and symbolic decomposit...Based on the two-dimensional three-temperature （2D3T） radiation diffusion equations and its discrete system, using the block diagonal structure of the three-temperature matrix, the reordering and symbolic decomposition parts of the RSMF method are replaced with corresponding block operation in order to improve the solution efficiency. We call this block form method block RSMF （in brief, BRSMF） method. The new BRSMF method not only makes the reordering and symbolic decomposition become more effective, but also keeps the cost of numerical factorization from increasing and ensures the precision of solution very well. The theoretical analysis of the computation complexity about the new BRSMF method shows that the solution efficiency about the BRSMF method is higher than the original RSMF method. The numerical experiments also show that the new BRSMF method is more effective than the original RSMF method.展开更多
目的对比肩峰下撞击综合征(SIS)的康复治疗方案,旨在寻找一种更为合理、更为有效、更为可行、重复性高的保守治疗SIS的方案。方法应用Biodex system 4多关节等速测评肩部肌群肌力及姿势评估,发现失衡的肩部肌肉,观察组48例应用肌肉调衡...目的对比肩峰下撞击综合征(SIS)的康复治疗方案,旨在寻找一种更为合理、更为有效、更为可行、重复性高的保守治疗SIS的方案。方法应用Biodex system 4多关节等速测评肩部肌群肌力及姿势评估,发现失衡的肩部肌肉,观察组48例应用肌肉调衡训练结合神经肌肉关节促进法治疗SIS,并与46例应用神经肌肉关节促进法治疗对照,并用HSS肩关节评分系统、JOA肩关节疾患治疗成绩判定标准评分评估疗效,应用SPSS 20.0版统计学软件进行统计分析。结果94例患者完成评估治疗,其中观察组完成48例,对照组完成46例。观察组治疗后HSS评分(86.40±8.83)分,JOA评分(88.25±7.33)分;对照组治疗后HSS评分(68.93±11.84)分,JOA评分(78.09±6.79)分。经统计学计算,两组治疗后HSS评分、JOA评分均上升(t=-32.881、-28.098、-22.680、-26.646,P<0.05),且观察组的HSS评分、JOA评分均高于对照组(t=8.130、6.965,P<0.05)。结论治疗SIS的两种保守方案均有效,但应用肌肉调衡训练结合神经肌肉关节促进法的疗效明显优于单一应用神经肌肉关节促进法,且经济有效、容易掌握、利于推广,是一种较合理的可行的SIS的康复治疗方案。展开更多
基金supported by the National Basic Research Program (No. 2005CB321702)the China Outstanding Young Scientist Foundation (No. 10525102)the National Natural Science Foundation (No.10471146, No. 10571059 and No. 10571060), P.R. China
文摘The Hermitian and skew-Hermitian splitting （HSS） method is an unconditionally convergent iteration method for solving large sparse non-Hermitian positive definite system of linear equations. By making use of the HSS iteration as the inner solver for the Newton method, we establish a class of Newton-HSS methods for solving large sparse systems of nonlinear equations with positive definite Jacobian matrices at the solution points. For this class of inexact Newton methods, two types of local convergence theorems are proved under proper conditions, and numerical results are given to examine their feasibility and effectiveness. In addition, the advantages of the Newton-HSS methods over the Newton-USOR, the Newton-GMRES and the Newton-GCG methods are shown through solving systems of nonlinear equations arising from the finite difference discretization of a two-dimensional convection-diffusion equation perturbed by a nonlinear term. The numerical implemen- tations also show that as preconditioners for the Newton-GMRES and the Newton-GCG methods the HSS iteration outperforms the USOR iteration in both computing time and iteration step.
基金Project supported by the State Key Laboratory of Scientific/Engineering Computing,Chinese Academy of Sciencesthe International Science and Technology Cooperation Program of China(2010DFA14700)the National Natural Science Foundation of China(11071192)
文摘白中治等提出了解非埃尔米特正定线性方程组的埃尔米特和反埃尔米特分裂(HSS)迭代方法(Bai Z Z,Golub G H,Ng M K.Hermitian and skew-Hermitian splitting methodsfor non-Hermitian positive definite linear systems.SIAM J.Matrix Anal.Appl.,2003,24:603-626).本文精确地估计了用HSS迭代方法求解广义鞍点问题时在加权2-范数和2-范数下的收缩因子.在实际的计算中,正是这些收缩因子而不是迭代矩阵的谱半径,本质上控制着HSS迭代方法的实际收敛速度.根据文中的分析,求解广义鞍点问题的HSS迭代方法的收缩因子在加权2-范数下等于1,在2-范数下它会大于等于1,而在某种适当选取的范数之下,它则会小于1.最后,用数值算例说明了理论结果的正确性.
文摘提出了求解广义Lyapunov方程的HSS(Hermitian and skew-Hermitian splitting)迭代法,分析了该方法的收敛性,给出了收敛因子的上界.为了降低HSS迭代法的计算量,提出了求解广义Lyapunov方程的非精确HSS迭代法,并分析其收敛性.数值结果表明,求解广义Lyapunov方程的HSS迭代法及非精确HSS迭代法是有效的.
基金supported by the National Natural Science Foundation of China(GrantNos.61202098,61033009,61170309,91130024,and 11171039)the China Tianyuan Mathematics Youth Fund(GrantNo.11226337)
文摘Based on the two-dimensional three-temperature （2D3T） radiation diffusion equations and its discrete system, using the block diagonal structure of the three-temperature matrix, the reordering and symbolic decomposition parts of the RSMF method are replaced with corresponding block operation in order to improve the solution efficiency. We call this block form method block RSMF （in brief, BRSMF） method. The new BRSMF method not only makes the reordering and symbolic decomposition become more effective, but also keeps the cost of numerical factorization from increasing and ensures the precision of solution very well. The theoretical analysis of the computation complexity about the new BRSMF method shows that the solution efficiency about the BRSMF method is higher than the original RSMF method. The numerical experiments also show that the new BRSMF method is more effective than the original RSMF method.
文摘目的对比肩峰下撞击综合征(SIS)的康复治疗方案,旨在寻找一种更为合理、更为有效、更为可行、重复性高的保守治疗SIS的方案。方法应用Biodex system 4多关节等速测评肩部肌群肌力及姿势评估,发现失衡的肩部肌肉,观察组48例应用肌肉调衡训练结合神经肌肉关节促进法治疗SIS,并与46例应用神经肌肉关节促进法治疗对照,并用HSS肩关节评分系统、JOA肩关节疾患治疗成绩判定标准评分评估疗效,应用SPSS 20.0版统计学软件进行统计分析。结果94例患者完成评估治疗,其中观察组完成48例,对照组完成46例。观察组治疗后HSS评分(86.40±8.83)分,JOA评分(88.25±7.33)分;对照组治疗后HSS评分(68.93±11.84)分,JOA评分(78.09±6.79)分。经统计学计算,两组治疗后HSS评分、JOA评分均上升(t=-32.881、-28.098、-22.680、-26.646,P<0.05),且观察组的HSS评分、JOA评分均高于对照组(t=8.130、6.965,P<0.05)。结论治疗SIS的两种保守方案均有效,但应用肌肉调衡训练结合神经肌肉关节促进法的疗效明显优于单一应用神经肌肉关节促进法,且经济有效、容易掌握、利于推广,是一种较合理的可行的SIS的康复治疗方案。
