B-矩阵线性互补问题的误差界估计

利用严格对角占优M-矩阵的逆矩阵的无穷大范数的范围,给出了B-矩阵线性互补问题误差界新的估计式.相应数值算例表明了结果的有效性.     

B-矩阵线性互补问题误差界的上界序列

利用严格对角占优M-矩阵的逆矩阵的无穷大范数的范围,给出了B-矩阵线性互补问题解的误差界新的上界估计序列,理论证明了新估计式优于已有文献的结果.相应数值算例表明了结果的有效性.     

弱链对角占优B-矩阵线性互补问题的误差界估计

利用弱链对角占优M-矩阵的逆矩阵的无穷大范数的范围,给出了弱链对角占优B-矩阵线性互补问题误差界新的估计式.理论证明及数值算例均表明所得估计改进了某些现有结果.     

严格对角占优矩阵的行列式估计

本文研究了严格对角占优矩阵的行列式估计问题,利用矩阵的逐次降阶法获得了严格对角占优矩阵的几个行列式估计式,并对特殊的严格对角占优矩阵的情形进行了加强.     

严格α-对角占优M-矩阵A的‖A~(-1)‖_∞的上界估计

针对逆矩阵的无穷范数的上界估计问题,利用严格对角占优M-矩阵逆的无穷范数的上界,给出了严格α-对角占优M-矩阵A的||A~(-1)||_∞的单调递减的上界序列,理论证明及数值分析均表明所得估计改进了某些现有结果.     

几类非奇H-矩阵的行列式估计

非奇H-矩阵在数学物理、控制论、电力系统理论及经济学等许多领域有着重要的研究价值和实用价值.本文利用矩阵逆元素估计、矩阵的逐次降阶法及递归,给出严格对角占优矩阵、广义严格对角占优矩阵等几类非奇H-矩阵的行列式上下界的估计式.改进了已有的一些相关结果,并用数值算例说明文中结果的有效性.     

严格双对角占优矩阵行列式的上下界估计

严格双对角占优矩阵的行列式计算是数值代数中的热点问题. 本文首先将严格双对角占优矩阵右乘一个正对角矩阵, 使其化为严格对角占优矩阵, 其次对严格对角占优矩阵行列式的上下界进行估计, 从而得到严格双对角占优矩阵行列式的上下界估计. 最后通过数值算例表明所得估计是有效的.     

对角占优矩阵直积的一些性质

给出了对角占优矩阵直积的一些对角占优性质以及∞-范数估计式.     

严格对角占优M-矩阵的逆矩阵的无穷大范数的新上界

<正>1引言M-矩阵不仅是矩阵论和计算数学的重要研究课题之一,而且在物理学、生物学、经济数学等诸多领域有着重要的应用价值.受这些应用背景的影响,最近,许多专家和学者对严格对角占优M-_矩阵A的逆矩阵的无穷大范数‖A~(-1)‖_∞的上界进行了广泛探讨,并给出了一些很好的估计式[1—4].本文继续这个问题的研究,给出了‖A~(-1)‖_∞的上界新的估计式,这些估计式改进了文[2,3,4]中的相应结果.     

广义严格对角占优矩阵的一组判定条件

以M-矩阵以及α-对角占优矩阵为工具,对0≤α≤1,借助Hlder不等式给出了广义严格对角占优矩阵以及非奇异M-矩阵的几则新的充分条件,拓广了近期的一些相关结果,并用数值例子说明这些结果的有效性.     

Some new inequalities involving the Hadamard product of an M-matrix and its inverse

Acta Mathematicae Applicatae Sinica, English Series - For the Hadamard product of an M-matrix and its inverse, some new lower bounds on the minimum eigenvalue are given. These bounds can improve...     

Bounds for norms of the matrix inverse and the smallest singular value

In the first part, we obtain two easily calculable lower bounds for ‖A^-1‖, where ‖·‖ is an arbitrary matrix norm, in the case when A is an M-matrix, using first row sums and then column sums. Using those results, we obtain the characterization of M-matrices whose inverses are stochastic matrices. With different approach, we give another easily calculable lower bounds for ‖A^-1‖_∞ and ‖A^-1‖₁ in the case when A is an M-matrix. In the second part, using the results from the first part, we obtain our main result, an easily calculable upper bound for ‖A^-1‖₁ in the case when A is an SDD matrix, thus improving the known bound. All mentioned norm bounds can be used for bounding the smallest singular value of a matrix.     

Some Characterizations of a Class of M-matrices

ＳｏｍｅＣｈａｒａｃｔｅｒｉｚａｔｉｏｎｓｏｆａＣｌａｓｓｏｆ　Ｍ－ｍａｔｒｉｃｅｓＬｉＷｅｎ（黎稳）ａｎｄＺｈａｎｇＭｏｕｃｈｅｎｇ（张谋成）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ,ＳｏｕｔｈＣｈｉｎａＮｏｒｍａｌＵｖｉｖｅｒｓｉｔｙ,Ｇ...     

M-矩阵的性质与Hadamard-Fisher不等式的注记

主要研究了两个M-矩阵的比较性质与不等式,给出了M-矩阵与逆M-矩阵Hadamard-Fisher不等式等式成立的矩阵结构.     

判定非奇异M-矩阵的一个直接算法

给出了判定非奇异M-矩阵的一个直接算法.数值例子表明应用该算法可有效地判定一个给定矩阵是否为非奇异M-矩阵.     

Entrywise perturbation theory for diagonally dominant M-matrices with applications

Summary. This paper introduces a new perspective on the study of computational problems related to diagonally dominant M-matrices by establishing some new entrywise perturbation results. If a diagonally dominant M-matrix is perturbed in a way that each off-diagonal entry and its row sums (i.e. the quantities of diagonal dominance) have small relative errors, we show that its determinant, cofactors, each entry of the inverse and the smallest eigenvalue all have small relative errors. The error bounds are given and they do not depend on any condition number. Applying this result to the studies of electrical circuits and tail probabilities of a queue whose embedded Markov chains is of GI/M/1 type, we discuss the relative sensitivity of the operating speed of circuits and of the percentile of the queue length, respectively. Received January 17, 2000 / Published online June 7, 2001     

ON THE SPECTRAL PROPERTIES OF M-MATRICES AND ITS APPLICATIONS

1.IntroductionAndPreliminariesThespectralpropertiesofM-matricesplayanimportantroleinnonnegativemainstheory,andhavebeenappliedtostudythenumericalsolutionoflinearsystems.Recentlylmanyarticleshavediscussedwiththistopics(see[l--5]).ThepurposeofthispaperistoestablishthespectralinequalitiesofsingularM-matrices.ByapplyingthesepropertiesweanswerpartiallyanopenproblemandsolveanopenproblemposedbySchneiderin[4,5],somerecelltresultI2'4'6]onsplittingsofanM-matrixarealsoimproved.Allnotationsanddefinitio…     

A DIRECT ALGORITHM FOR DISTINGUISHING NONSINGULAR M-MATRIX AND H-MATRIX

A direct algorithm is proposed by which one can distinguish whether a matrix is an M-matrix (or H-matrix) or not quickly and effectively. Numerical examples show that it is effective and convincible to distinguish M-matrix (or H-matrix) by using the algorithm.     

M-矩阵线性互补问题模系多分裂迭代方法的收敛性

首先证明了M-矩阵的H-相容分裂都是正则分裂,反之不成立.这表明对于M-矩阵而言,其正则分裂包含H-相容分裂.然后针对系数矩阵为M-矩阵的线性互补问题,建立了两个收敛定理:一是模系多分裂迭代方法关于正则分裂的收敛定理;二是模系二级多分裂迭代方法关于外迭代为正则分裂和内迭代为弱正则分裂的收敛定理.