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岳嵘 《数学的实践与认识》2012,42(19)
非奇H-矩阵在数值分析和矩阵理论的研究中非常重要,但实际判定一个非奇异H-矩阵却非常困难.给出一类非奇异H-矩阵新的判定条件,改进了近期的相关结果,并用数值例子说明了结果判定范围的更广泛性. 相似文献
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庹清 《高校应用数学学报(A辑)》2019,34(3)
利用新的正对角因子,得出几个非奇异H-矩阵新的判定条件,改进和推广了"非奇异H-矩阵的实用新判定"一文的主要结果,并用数值例子说明了结论的有效性. 相似文献
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非奇异H-矩阵是在数值分析,矩阵理论,控制论等众多领域有着重要应用的一类特殊矩阵.文中通过进一步划分区域和迭代的方法,给出了一组非奇异H-矩阵的迭代判别条件,推广和改进了相关已有结果,并用数值算例说明这种判定方法有效性. 相似文献
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利用矩阵指标集的k-级划分和子矩阵的谱半径,给出了正定条件下广义H-矩阵的一组判定条件,当块矩阵退化为点矩阵时,这些条件即为非奇异H-矩阵的充分条件.这些结果改进了近期的相关结果,并用数值算例说明本文判定条件的有效性. 相似文献
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结合矩阵自身的元素,构造了含参数的迭代公式,进而细分了矩阵非对角占优行指标集.利用广义严格α-对角占优矩阵与非奇异H-矩阵的关系,给出了非奇异H-矩阵一组新的细分迭代判定准则,推广和改进了已有的结果,通过数值算例说明了结果的优越性. 相似文献
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通过构造新的正对角因子元素,本文给出了几个判定非奇异H-矩阵新的充分条件,改进和推广了"一类非奇异H-矩阵判定的新条件"一文的主要结果,并用数值例子说明了文中结果判定范围的更加广泛性. 相似文献
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利用α2-双对角占优理论,给出了几个判定非奇异H-矩阵的充分条件,扩大了非奇异H-矩阵的判定范围,并给出了相应的数值算例说明结果的有效性. 相似文献
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In this paper, a set of criteria of nonsingular H-matrices are discussed. The paper introduces the concept of α-bidiagonally dominant matrices and gives an equivalent condition of strictly α-bidiagonally dominant matrices. According to the given condition, some new practical criteria of nonsingular H-matrices are obtained. Finally, some numerical examples are given. 相似文献
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In this paper, we consider convex sets of real matrices and establish criteria characterizing these sets with respect to certain matrix properties of their elements. In particular, we deal with convex sets of P-matrices, block P-matrices and M-matrices, nonsingular and full rank matrices, as well as stable and Schur stable matrices. Our results are essentially based on the notion of a block P-matrix and extend and generalize some recently published results on this topic. 相似文献
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Let M(A) denote the comparison matrix of a square H-matrix A, that is, M(A) is an M-matrix. H-matrices such that their comparison matrices are nonsingular are well studied in the literature. In this paper, we study characterizations of H-matrices with either singular or nonsingular comparison matrices. The spectral radius of the Jacobi matrix of M(A) and the generalized diagonal dominance property are used in the characterizations. Finally, a classification of the set of general H-matrices is obtained. 相似文献
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The class of real matrices which are both monotone (inverse positive) and positive stable is investigated. Such matrices, called N-matrices, have the well-known class of nonsingular M-matrices as a proper subset. Relationships between the classes of N-matrices, M-matrices, nonsingular totally nonnegative matrices, and oscillatory matrices are developed. Conditions are given for some classes of matrices, including tridiagonal and some Toeplitz matrices, to be N-matrices. 相似文献
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Rafael Bru Ljiljana Cvetković Vladimir Kostić Francisco Pedroche 《Central European Journal of Mathematics》2010,8(1):32-40
This paper deals with some properties of α1-matrices and α2-matrices which are subclasses of nonsingular H-matrices. In particular, new characterizations of these two subclasses are
given, and then used for proving algebraic properties related to subdirect sums and Hadamard products. 相似文献
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The paper studies the convergence of some block iterative methods for the solution of linear systems when the coefficient matrices are generalized H-matrices. A truth is found that the class of conjugate generalized H-matrices is a subclass of the class of generalized H-matrices and the convergence results of R. Nabben [R. Nabben, On a class of matrices which arises in the numerical solution of Euler equations, Numer. Math. 63 (1992) 411–431] are then extended to the class of generalized H-matrices. Furthermore, the convergence of the block AOR iterative method for linear systems with generalized H-matrices is established and some properties of special block tridiagonal matrices arising in the numerical solution of Euler equations are discussed. Finally, some examples are given to demonstrate the convergence results obtained in this paper. 相似文献
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In this paper we characterize the nonnegative nonsingular tridiagonal matrices belonging to the class of inverse M-matrices. We give a geometric equivalence for a nonnegative nonsingular upper triangular matrix to be in this class. This equivalence is extended to include some reducible matrices. 相似文献
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Wallace C. Pye 《Mathematical Programming》1992,57(1-3):439-444
This paper demonstrates that within the class of thosen × n real matrices, each of which has a negative determinant, nonnegative proper principal minors and inverse with at least one positive entry, the class ofQ-matrices coincides with the class of regular matrices. Each of these classes of matrices plays an important role in the theory of the linear complementarity problem. Lastly, analogous results are obtained for nonsingular matrices which possess only nonpositive principal minors. 相似文献