非奇异H-矩阵的简捷判定

1 引言 非奇异H-矩阵是应用广泛的一类特殊矩阵,它在矩阵理论、数量经济学和数学物理等诸多领域发挥着重要作用.然而其实际判别却比较困难.文献[1-9]给出了一些比较实用的判别方法.     

非奇H-矩阵的充要条件

推广了"非奇H-矩阵的条件"一文中的主要结果,得到一类特殊矩阵为非奇H-矩阵的充分必要条件.     

线性互补问题的SSOR多分裂算法

运用矩阵的SSOR多分裂和松弛迭代算法,提出了一类求解线性互补问题的数值解法.在一定条件下分析了算法的全局收敛性和松弛因子的范围,扩大了以往求解线性方程组的SSOR多分裂迭代算法的收敛区域.     

对称双对角占优矩阵及其应用

引进两类对称双对角占优矩阵,利用这一概念获得非奇H矩阵几个新的充分条件,从而扩大矩阵的判别范围,推广一些已有的结论,并通过数值例子说明所得结论的有效性.     

非奇异Ｈ 矩阵的充分条件

给出了几个非奇异H-矩阵的新的实用判定条件,扩大了H-矩阵判定的范围,并用数值算例说明了结果判定范围的广泛性.     

Convergence of nonstationary multisplitting methods using ILU factorizations

In this paper, we first study convergence of nonstationary multisplitting methods associated with a multisplitting which is obtained from the ILU factorizations for solving a linear system whose coefficient matrix is a large sparse H-matrix. We next study a parallel implementation of the relaxed nonstationary two-stage multisplitting method (called Algorithm 2 in this paper) using ILU factorizations as inner splittings and an application of Algorithm 2 to parallel preconditioner of Krylov subspace methods. Lastly, we provide parallel performance results of both Algorithm 2 using ILU factorizations as inner splittings and the BiCGSTAB with a parallel preconditioner which is derived from Algorithm 2 on the IBM p690 supercomputer.     

关于非奇异H-矩阵的一类充分条件

提出了一类局部双对角占优矩阵，并据此给出了其为非奇异H-矩阵的新判据，最后通过数值实例说明了所得结果的有效性。     

块H-矩阵的简捷判据

本文讨论了块H－矩阵的简捷判定问题，在适当的条件下，获得了一些直接利用矩阵元素判定块H－矩阵的条件，这些条件均由一些具体的计算公式表示，从而可以通过直接计算简捷地判定块H－矩阵。     

Some Simple Estimates for the Singular Values of Matrices

Abstract We first provide a simple estimate for ||A~(-1)||_∞ and ||A~(-1)||_1 of a strictly diagonally dominant matrixA. On the Basis of the result, we obtain an estimate for the smallest singular value of A. Secondly, by scalingwith a positive diagonal matrix D, we obtain some simple estimates for the smallest singular value of an H-matrix, which is not necessarily positive definite. Finally, we give some examples to show the effectiveness ofthe new bounds.     

Conditions of LU as M, H-matrix

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