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A note on a criterion for M-matrix

Computational Mathematics and Modeling, 2009
There are many ways to characterize \(M\)-matrices. One of these is: a real \(n\times n\) matrix \(A\) is an \(M\)-matrix if and only if all its off-diagonal entries are \(\leq0\) and all leading principal minors are positive. The authors present a further criterion which may be simpler to verify.
Hashimoto, Tomoaki, Amemiya, Takashi
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Accurate solutions of M-matrix Sylvester equations

Numerische Mathematik, 2011
The authors present a relative perturbation theory for an \(M\)-matrix Sylvester equation (MSE). Specifically, the MSE is meant by the matrix equation \(AX + XB = C\) where \(A\) and \(B\) have positive diagonal entries and nonpositive off-diagonal entries; \(P = I_m \otimes A + B^T \otimes I_n\) is a nonsingular \(M\)-matrix; and \(C\) is entry-wise ...
Jungong Xue, Shufang Xu, Ren-Cang Li
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Computing the Smallest Eigenvalue of an M-Matrix

SIAM Journal on Matrix Analysis and Applications, 1996
A computation of the smallest eigenvalue and the corresponding eigenvector of an irreducible nonsingular \(\text{M}\)-matrix \(A\) is considered. Section 2 introduces some lemmas for M-matrices. Sections 3 and 4 discuss perturbation theory for the eigenvalues and for each component of the corresponding eigenvector.
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Convergence of SSOR multisplitting method for an M-matrix

Journal of Applied Mathematics and Computing, 2007
The authors consider the multisplitting method and the relaxed multisplitting method for solving a linear system of equations with a large sparse \(M\)-matrix. They prove convergence results for both classes of methods under appropriate assumptions on the relaxation parameters.
Yun, Jae Heon, Han, Yu Du, Oh, Seyoung
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Preconditioned AOR Iterative Method for M-Matrix

2013 Ninth International Conference on Computational Intelligence and Security, 2013
In 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   +2 more
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