非奇异H矩阵的一个判定条件及一类实矩阵逆的无穷范数估计

通过理论证明,给出了判断一个矩阵为H矩阵的实用充分条件及一类实矩阵逆的无穷范数估计公式,并给出数值例子进行了说明.此结果对于判定系统的稳定性、特征值分布、线性方程组迭代解及矩阵范数估计等都具有重要的理论和实际意义.     

特殊拟α-双对角占优矩阵的讨论及其应用

定义了特殊拟-双对角占优矩阵,给出了严格特殊拟-双对角占优矩阵的等价表征。由此得到非奇异H-矩阵的判定条件,并用数值例子说明了判定条件的有效性。     

Relaxed parallel two-stage multisplitting methods II: Asynchronous version

Two classes of asynchronous relaxed parallel two-stage multisplitting methods based on extrapolated and AOR methods are studied for the solution of nonsingular linear systems, which are called asynchronous outer relaxed or inner relaxed parallel two-stage multisplitting methods. Convergence of these methods is studied for H-matrix. Almost all methods seen in literatures can be viewed as special cases of our methods.     

非奇异H-矩阵的一个简捷判别定理

设A=(aij)∈Cn×n,若存在α∈(0,1),使■i∈N,有|aii|≥Rαi(A)S1-αi(A)成立,则称A为α链对角占优矩阵。利用α-链对角占优矩阵、不可约α-链对角占优矩阵、广义严格α-链对角占优矩阵等概念及性质,给出了非奇异H-矩阵的一个简捷判别定理。从而改进和推广了相应的一些结果,并给出相应的数值例子说明结果的有效性。     

非奇异H-矩阵的充分条件

利用矩阵的结构信息和矩阵的α-对角占优性,给出了非奇异H-矩阵的两个充分条件,推广和改进了相关结果.     

H矩阵的Minkowski型不等式

用具体实例指出了文献[1]中给出的H矩阵的Minkowski型不等式的错误,同时修正了文献[1]中的错误,并拓广了H矩阵的Minkowski型不等式.     

基于反演设计的机械臂非奇异终端神经滑模控制

针对具有建模误差和不确定干扰的多关节机械臂的轨迹跟踪问题,设计反演非奇异终端神经滑模控制。该方案是采用能有限时间收敛的非奇异终端滑模面,根据滑模控制原理和反演方法设计反演滑模控制器;对于反演滑模控制系统中由于建模误差和不确定干扰造成的不确定因素的上界,设计径向基(Radial basis function, RBF)神经网络自适应律,在线估计不确定因素的上界;利用李亚普诺夫定理证明了系统的稳定性。仿真结果表明,该方法具有良好的轨迹跟踪性能,提高对于建模误差和不确定干扰等因素的鲁棒性,削弱了抖动。     

非奇异H矩阵的一组细分迭代判定条件

非奇异H矩阵是在科学和工程应用中经常遇到的一类特殊矩阵,研究其判定问题非常重要.本文根据α-链对角占优矩阵与非奇异H矩阵的关系,利用细分区间和构造迭代系数的思想,细分了矩阵的非对角占优行集合,给出了非奇异H矩阵的一组细分迭代判定条件,推广和改进了近期的一些结果.数值算例说明了该判定条件的有效性.     

Significance of K-dominance zone size and nonsingular stress field in brittle fracture

Stress intensity factor has been used to characterize the fracture toughness of a brittle material. This practice is apparently based on the assumption that the singular stress alone at the crack tip is responsible for fracture and that the nonsingular part of the near tip stress has no effect on fracture. In this study, mode I fracture experiments were conducted on a brittle material (PMMA) with four different specimen configurations. The result indicated that fracture toughness cannot be described by stress intensity alone and that a second parameter representing the influence of the nonsingular stress is needed. A two-parameter fracture model was proposed and validated with the experimental result. This two-parameter model was shown to be able to account for various effects created by specimen configurations, crack sizes, and loading conditions, on the fracture behavior of brittle materials.     

广义Ostrowski对角占优矩阵与非奇异H-矩阵的判定

设A=(aij)∈Cn×n,若α∈(0,1),使i∈N+,有|aii|≥Riα(A)S1i-α(A)成立,则称A为Ostrowski对角占优矩阵;推广Ostrowski对角占优矩阵的概念到广义Ostrowski对角占优矩阵;得到了判别非奇异H-矩阵的一个判定方法.进一步丰富和完善了Ostrowski对角占优矩阵和非奇异H-矩阵的理论.