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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
openaire   +2 more sources

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
openaire   +1 more source