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1.
正1引言设A=(a_(ij))∈C~(n×n),N={1,2,…,n}.记R_i(A)= sum |a_(ij)| from j≠i (i∈N),又记N_1=N_1(A)={i∈N:0|a_(ii)|≤R_i(A)},N_2=N_2(A)={i∈N:|a_(ii)R_i(A)}.定义1设A=(a_(ij))∈C~(n×n),如果|a_(ii)|R_i(A)(i∈N),则称A为严格对角占优矩阵.严格对角占优矩阵的集合记为D.如果存在n阶正对角矩阵D使得AD∈D,则称A为广义严格对角占优矩阵.广义严格对角占优矩阵的集合记为D.  相似文献   

2.
局部双对角占优矩阵的注记   总被引:5,自引:0,他引:5  
1引言非奇异H矩阵是计算数学、数学物理、控制论等领域中具有广泛应用的重要矩阵类,研究其充分条件自然引起人们的兴趣.文[1]中定义了一类局部双对角占优矩阵,并由此得到了非奇异H矩阵的判别方法.我们指出,文[1]所获充分条件中所给出的四个不等式条件,其中第四个不等式条件可蕴涵其余三个,进而定义了另一类局部双对角占优矩阵,并由此获得了非奇异H矩阵新的判别方法.设A=(a_(ij))∈C~(n×n),R_i(A)=sum from j≠i|a_(ij)|,i∈N={1,2,…,n}.若|a_(ii)|≥R_i(A),(?)i∈N,则称A为对角占优矩阵,记为A∈D_o;若不等式中每个不等号都是严格的,则称A为  相似文献   

3.
矩阵对角占优性的推广及应用   总被引:38,自引:1,他引:37  
§1.引言设 A=(a_(ij))_(n×n)为一复矩阵,若有一正向量 d=(d_1,d_2,…,d_n)~T 使得d_i|a_(ij)|≥sum from j≠1 d_j|a_(ij)|,(1)对每一 i∈N={1,2,…,n}都成立,则称 A 为广义对角占优矩阵,记为 A∈D_0~*;如若(1)式中每一不等号都是严格的,则称 A 为广义严格对角占优矩阵,记为 A∈D~*.特别地,当 d=(1,1,…,1)~T 时,A∈D_0~*及 A∈D~*即是通常的对角占优与严格对角占优,分别记作 A∈D_0及 A∈D.利用矩阵的对角占优性质讨论其特征值分布是矩阵论中的重要课题,文献[5]—[10]给出了这方面的重要结果.n 阶实方阵 A 称为 M-矩阵,如果 A具有形式:A=sI-B,s>ρ(B),其中 B 为 n 阶非负方阵,ρ(B)表 B 之谱半径,利用广义严格对角占优的概念,文[1]给出了 M-矩阵的等价表征:若 n 阶实方阵  相似文献   

4.
设A=(a_(ij))_(n×n)为n阶复矩阵,记 σ_i=sum from j=1,j≠i to n(|a_(ij)|,i=l,2,…,n)。若|a_(ij)|>σ_i(i=1,2,…n),则称A为(按行)严格对角占优阵,记为A∈D,若|a_(ii)|·|a_(jj)|>σ_iσ_j(i≠j,i,j=1,2,…,n)则称A为严格对角乘积占优阵,记为A∈D_p(在〔1〕中此类矩阵称为广义对角占优阵,并记为GD)。若存在非奇对角阵Q=diag(q_l,…,q_n)使Q~(-1)AQ∈D,则称A为准严格对角占优阵,记为A∈D′(见〔2〕)。若存在非奇对角阵Q=diag(q_1,…,q_n)使Q~(-1)AQ∈D_p,则称A为准严格对角乘积占优阵。记为A∈D′_p。  相似文献   

5.
广义严格对角占优阵的判定程序   总被引:3,自引:1,他引:2  
1 引言和符号 在本文中,均采用下列符号而不再重申.恒用N表示前n个自然数的集合;而用Mn(C)和Mn(R)分别表示所有n阶复矩阵和所有n阶实矩阵的集合. Z_N={A|A=(a_(ij))_(n×n)∈Mn(R),a_(ij)≤0,i,j∈N,i≠j},I恒表示单位矩阵. 如果A∈Mn(R)且A的所有元素都为非负实数,则称A为非负方阵,并记为A≥0;若A的所有元素都为正数,则称A为正矩阵,并记为A>0. 对A=(a_(ij))(n×n)∈Mn(C),令A_i(A)=sum from j=1 j≠i to n (|a_(ij)|(i=1、2…… n)) ;若把A的非零元用1代替 而得到—个n阶(0,1)矩阵。称为A的导出矩阵。记为;而把A的比较矩阵记为 u(A)=(b_(ij))_(n×n))其中b_(ij)=|a_(ij)|,b_(ij)=-|a_(ij)|(i,j∈N i≠j)  相似文献   

6.
1引言 设A=(a_η)∈Cm~(3n),若存在正对角阵D.使得AD为严格对角占优矩阵,则A称为广义严格对角占优矩阵,记作A∈SGDDM.  相似文献   

7.
非奇异H-矩阵的新判据   总被引:1,自引:0,他引:1  
1引言与记号设A=(a_(ij))∈C~(n×n),记N={1,2,…,n},∧_i(?)∧_i(A)=sum from j≠i|a_(ij)|,S_i(?)S_i(A)=sum from j≠i|a_(ij)|,(?)i,j∈N。若|a_(ij)>∧_i(A),(?)i∈N,则称A为严格对角占优矩阵。  相似文献   

8.
连对角占优矩阵的一些性质   总被引:29,自引:3,他引:29  
沈光星 《计算数学》1990,12(2):132-135
设A=(a_(ij))_(n×n)∈C~(n,n),.记Λ_i=sum from (i≠1 j≠i) to n(|a_(ij)|,)i=?,称|a_(ii)|≥Λ_i的行为占优行,|a_(ii)|>Λ_i的行为严格占优行,|a_(ii)|<Λ_i的行为非占优行. 若A为对角占优阵,记为A∈D_0;若A为严格对角占优阵,记为A∈E;若A为不可约对角占优阵,记为A∈F;若A为广义对角占优阵,记为A∈GD_0;若A为广义严格对角占优阵,记为A∈GE.  相似文献   

9.
有广义对角占优系数矩阵的齐次线性方程组   总被引:2,自引:0,他引:2  
引言与定义 本文限于考虑无零行零列的n×n,(n>2)复矩阵,我们采用以下记号:N={1,2,…,n};R_i=sum from j∈N-(i)│a_(ij)│;C_i=sum from j∈N-(i)│a_(ij)│;S_i(a)=R_i~HC_i~(1-a),j∈N,a∈[0.1];A∈Z,表示A有全部非正的非对角元的n×n实方阵。  相似文献   

10.
1引言在计算数学、数学物理、控制论与矩阵论中,非奇异H-矩阵是有着重要应用的一类特殊矩阵,有关其数值判定也一直是矩阵计算的重要课题,不少学者对此进行了研究,得到了许多结果,如文[1]-[10]都给出一些比较实用的判别方法.本文另提出了一些新的实用性判别,进一步改进了文[1]的主要结果.用Cn×n表示n阶复矩阵集,设A=(aij)∈Cn×n,记,若|aii|≥Λi(i=1,2,…,n)(本文用Λi表示Λi(A)),则称A为对角占优矩阵;如果每个不等号都为严格成立,则称A为严格对角占优矩阵,记A∈D;若存在正对角阵X,使得AX为严格对角占优矩阵,则称A为广义严格对角占优阵,记A∈D.设A∈Zn×n={(aij)∈Cn×n|aij≤0,i≠j;i,j∈N},若A=sI-B,s>ρ(B),其中B为非负方阵,ρ(B)表示B的谱半径,则称A为非奇异M-矩阵.若A∈Cn×n的比较矩阵M(A)=(mij)为非奇异M-矩阵,则称A为非奇异H-矩阵,其中  相似文献   

11.
12.
Summary DCT Given a finite set of points in an Euclidean space the \emph{spanning tree} is a tree of minimal length having the given points as vertices. The length of the tree is the sum of the distances of all connected point pairs of the tree. The clustering tree with a given length of a given finite set of points is the spanning tree of an appropriately chosen other set of points approximating the given set of points with minimal sum of square distances among all spanning trees with the given length. DCM A matrix of real numbers is said to be column monotone orderable if there exists an ordering of columns of the matrix such that all rows of the matrix become monotone after ordering. The {\emph{monotone sum of squares of a matrix}} is the minimum of sum of squares of differences of the elements of the matrix and a column monotone orderable matrix where the minimum is taken on the set of all column monotone orderable matrices. Decomposition clusters of monotone orderings of a matrix is a clustering ofthe rows of the matrix into given number of clusters such that thesum of monotone sum of squares of the matrices formed by the rowsof the same cluster is minimal.DCP A matrix of real numbers is said to be column partitionable if there exists a partition of the columns such that the elements belonging to the same subset of the partition are equal in each row. Given a partition of the columns of a matrix the partition sum of squares of the matrix is the minimum of the sum of square of differences of the elements of the matrix and a column partitionable matrix where the minimum is taken on the set of all column partitionable matrices. Decomposition of the rows of a matrix into clusters of partitions is the minimization of the corresponding partition sum of squares given the number of clusters and the sizes of the subsets of the partitions.  相似文献   

13.
The theory of long-term damageability of a homogeneous material is generalized to the case of an orthotropic fibrous composite material with a stochastic structure. Equations of mechanics of microinhomogeneous media of this structure form the base of the theory. The process of damage of components of a composite is modeled by the formation of stochastically located micropores. The criterion of fracture of a unit microvolume is characterized by its long-term strength determined by the dependence of the time of brittle fracture on the degree of closeness of the equivalent stress to its limit value, which characterizes the short-term strength on the basis of the Huber–von Mises criterion accepted as an arbitrary function of coordinates. Efficient deformation properties and the stress-strain state of an orthotropic fibrous composite with microdamages in components are determined on the base of stochastic equations of elasticity of orthotropic media. For given macrostresses and macrostrains and an arbitrary moment of time, balance equations of damage (porosity) of components are formulated. On the basis of the iteration method, we construct algorithms for calculating dependences of microdamage of components of an orthotropic fibrous material on time and dependences of macrostresses or macrostrains on time and obtain the corresponding curves for the case of a bounded function of the long-term microstrength, which is approximated by an exponential law.  相似文献   

14.
15.
Three methods of the optimal planning of the inspection and maintenance of offshore structures are described. The models are based on respectively: the maximization of the effect of inspections, measured by the total importance value of the errors detected, subject to a given total economical budget; the minimization of the total costs of obtaining respectively: a given importance value of errors detected or given numbers of inspections of various types. Special selections of the importance values of structural elements give problems of the maximization of the reliability of the structural system, or the minimization of the economical consequences of failures, or the minimization of the sum of the costs of inspections and failure-consequences, subject to a given total failure probability of the system.Different failure types of elements and time schedules of inspections can be included in the model.An extension of the incremental method of Fox is applied, and an evaluation measure is given for the calculation of bounds of the optimal objective value, or given numbers of inspections are planned by application of continuous linear programming with integral solutions.  相似文献   

16.
我国医疗费用增长与医疗设备投入的相关性研究   总被引:3,自引:0,他引:3  
近年来我国卫生总费用占GDP的比例增长很快,而在卫生费用结构上则发生政府投入下降和个人支出的上升。本文采集了大量的统计数据,采用统计相关性研究的方法,论证了医疗设备规模的不断扩大是导致医疗费用上升的主要因素之一;医疗设备的快速增长与医院维修费用投入的增长直接相关,而引起医疗设备维修大量投入的主要原因则是故障期内医疗设备的非正常闲置。本文通过对个人卫生费用的上升、医疗设备规模的扩大及其医疗设备维修投入费用增加相关性的分析,说明了在这种关系下,十分有必要研究医院医疗设备维修体系,以在卫生投入和患者权益上达到平衡。  相似文献   

17.
18.
In this paper, we give an operator parameterization for the set of dilations of a given pair of dual g-frames and the set of dilations of pairs of dual g-frames of a given g-frame. In particular, for the dilations of a given pair of dual g-frames, we introduce the concept of joint complementary g-frames and prove that the joint complementary g-frames of a pair of dual g-frames are unique in the sense of joint similarity, which then helps to obtain a sufficient condition such that the complementary g-frames of a g-frame are unique in the sense of similarity and show that the set of dilations of a given dual g-frame pair are parameterized by a set of invertible diagonal operators. For the dilations of pairs of dual g-frames, we prove that the set of dilations of pairs of dual g-frames are parameterized by a set of invertible upper triangular operators.  相似文献   

19.
Problems of the joint optimization of the shape and distribution along the meridian of the thickness of membrane shells of revolution under the action of axisymmetric loads are considered, taking account of the constraints concerning the strength of the shell and the volume of its cavity. General formulations of problems of the optimal design of shells of revolution are given and the optimal shape of a shell and the corresponding thickness distribution are investigated. Results of the exact solution of problems of the optimal design of closed shells of revolution when there is an internal pressure are presented. The simultaneous introduction of two control functions, describing the shape of the shell and the distribution of its thickness, not only ensures a substantial reduction in the mass of a shell but also leads to significant mathematical simplifications, which enable the solution of the optimization problem being considered to be obtained in an analytical form.  相似文献   

20.
The problem of determining the parameters of the law of distribution of load-carrying capacity of fiberglass-reinforced plastic tubes, obtained by the method of winding impregnated cloth on a mandrel, has been dealt with. The parameters of the law of distribution of the load-carrying capacity are determined by the statistical model analysis of the problem with the help of a computer, applying the unified strength criterion of Gol'denblat—Kopnov and on the basis of the results of breaking and control tests along with the use of the method of graphical analysis of the risk function of distribution of the load-carrying capacity.  相似文献   

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