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A note on a criterion for M-matrix
Computational Mathematics and Modeling, 2009The aim of this work is to propose a novel method for confirming whether a given matrix is an M-matrix. The proposed method has the advantage of allowing one to deduce whether the matrix whose entry consists of the functional order is an M-matrix.
Tomoaki Hashimoto, Takashi Amemiya
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Convergence of SSOR multisplitting method for an M-matrix [PDF]
Journal of Applied Mathematics and Computing, 2007 In this paper, we study the convergence of both the multisplitting method and the relaxed multisplitting method associated with SOR or SSOR multisplittings for solving a linear system whose coefficient matrix is an M-matrix.
Seyoung Oh, Yu Du Han, Jae Heon Yun
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Criteria for transforming a Z-matrix into an M-matrix
Optimization Methods and Software, 1992A characterization of M-matrices is given by means of a special algorithm in the ABS class for linear systems. The effects of changes in the entries of the coefficient matrix are investigated. An application to the classical static Leontief and Sraffa input- output economic model is presented together with numerical results on a real case using an IBM ...
Torriero, Anna, Abaffy, J, Bertocchi, M.
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On a quadratic matrix equation associated with an M-matrix [PDF]
IMA Journal of Numerical Analysis, 2003 We study the quadratic matrix equation X 2 - EX - F = 0, where E is diagonal and F is an M-matrix. Quadratic matrix equations of this type arise in noisy Wiener-Hopf problems for Markov chains. The solution of practical interest is a particular M-matrix solution.
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Preconditioned AOR Iterative Method for M-Matrix
2013 Ninth International Conference on Computational Intelligence and Security, 2013In this paper, we propose a new selection mode of 'r, t' for the preconditioner I+C and analyze the convergence performance of the preconditioned AOR iterative method induced by this preconditioner. For a nonsingular M-matrix, we show that the preconditioned AOR iterative method with this choice and the preconditioned methods advised by Evans et al ...
Qiufang Xue, Xiaoguang Liu, Xingbao Gao
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Computing the Smallest Eigenvalue of an M-Matrix
SIAM Journal on Matrix Analysis and Applications, 1996A computation of the smallest eigenvalue and the corresponding eigenvector of an irreducible nonsingular M-matrix $A$ is considered. It is shown that if the entries of $A$ are known with high relative accuracy, the smallest eigenvalue and each component of the corresponding eigenvector will be determined to high relative accuracy.
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1989
We now proceed to consider some main properties of M-matrices. They are of general interest, and besides they bear some direct relationship to discretization methods as will be seen later on. Referring to the literature, we shall omit the proofs, which are far from being elementary.
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We now proceed to consider some main properties of M-matrices. They are of general interest, and besides they bear some direct relationship to discretization methods as will be seen later on. Referring to the literature, we shall omit the proofs, which are far from being elementary.
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Communications in Theoretical Physics, 1991
We discuss the relations between the K–M matrix and the masses of the quarks and leptons in the case of four generations, and give the exact expression of the K–M matrix in terms of the masses of quarks and leptons. The requirement that the theoretical and experimental values of the K–M ,matrix are consistent leads to an allowed range of quark masses ...
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We discuss the relations between the K–M matrix and the masses of the quarks and leptons in the case of four generations, and give the exact expression of the K–M matrix in terms of the masses of quarks and leptons. The requirement that the theoretical and experimental values of the K–M ,matrix are consistent leads to an allowed range of quark masses ...
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Accurate solutions of M-matrix Sylvester equations
Numerische Mathematik, 2011This paper is concerned with a relative perturbation theory and its entrywise relatively accurate numerical solutions of an M-matrix Sylvester equation AX + XB = C by which we mean both A and B have positive diagonal entries and nonpositive off-diagonal entries and $${P=I_m \otimes A+B^{\rm T} \otimes I_n}$$ is a nonsingular M-matrix, and C is ...
Ren-Cang Li, Shu-Fang Xu, Jungong Xue
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2017
As mentioned in the previous chapter, modern finite difference schemes must (i) be at least of second order of approximation in all independent variables; (ii) be unconditionally stable; (iii) preserve nonnegativity of the solution. To achieve these goals, it became a common practice to involve a special apparatus of matrix theory that operates with so-
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As mentioned in the previous chapter, modern finite difference schemes must (i) be at least of second order of approximation in all independent variables; (ii) be unconditionally stable; (iii) preserve nonnegativity of the solution. To achieve these goals, it became a common practice to involve a special apparatus of matrix theory that operates with so-
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