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M-matrix and inverse M-matrix extensions
Special Matrices, 2020 A class of matrices that simultaneously generalizes the M-matrices and the inverse M-matrices is brought forward and its properties are reviewed. It is interesting to see how this class bridges the properties of the matrices it generalizes and provides a
McDonald J.J. +6 more
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Extended Perron complements of M-matrices
AIMS Mathematics, 2023 This paper aims to consider the extended Perron complements for the collection of M-matrices. We first exhibit the connection between the extended Perron complements of M-matrices and nonnegative matrices.
Qin Zhong, Chunyan Zhao
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Row Stochastic Matrices and Linear Preservers of Matrix Majorization $T:\mathbb{R}_{m} \rightarrow \mathbb{R}_{n}$ [PDF]
Mathematics Interdisciplinary Research, 2023 A nonnegative square and real matrix $R$ is a row stochastic matrix if the sum of the entries of each row is equal to one. Let $x$, $y \in \mathbb{R}_{n}$.
Ahmad Mohammadhasani +2 more
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Two new generalized iteration methods for solving absolute value equations using M-matrix
AIMS Mathematics, 2022 In this paper, we present two new generalized Gauss-Seidel iteration methods for solving absolute value equations Ax−|x|=b, where A is an M-matrix. Furthermore, we demonstrate their convergence under specific assumptions.
Rashid Ali +3 more
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Electronic Research Archive, 2022 Consider the problem of finding the maximal nonpositive solvent $ \varPhi $ of the quadratic matrix equation (QME) $ X^2 + BX + C = 0 $ with $ B $ being a nonsingular $ M $-matrix and $ C $ an $ M $-matrix such that $ B^{-1}C\ge 0 $. Such QME arises from
Cairong Chen
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New lower bounds of the minimum eigenvalue for the Fan product of several M-matrices
AIMS Mathematics, 2023 In this study, we generalize the definition of the Fan product of two M-matrices to any $ k $ M-matrices $ {{A}_{1}}, {{A}_{2}}, \cdots, {{A}_{k}} $ of order $ n $.
Qin Zhong
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Matrix Analysis for Continuous-Time Markov Chains
Special Matrices, 2021 Continuous-time Markov chains have transition matrices that vary continuously in time. Classical theory of nonnegative matrices, M-matrices and matrix exponentials is used in the literature to study their dynamics, probability distributions and other ...
Le Hung V., Tsatsomeros M. J.
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Electronic Journal of Qualitative Theory of Differential Equations, 2020 By employing the notion of M-matrices and Banach's contraction mapping theorem, we provide complete characterisation of the existence and uniqueness of an equilibrium of a Cohen–Grossberg–Hopfield-type neural network endowed with multiple distributed ...
Israel Ncube
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On the Iterative Methods for the Solution of Three Types of Nonlinear Matrix Equations
Mathematics, 2023 In this paper, we investigate the iterative methods for the solution of different types of nonlinear matrix equations. More specifically, we consider iterative methods for the minimal nonnegative solution of a set of Riccati equations, a nonnegative ...
Ivan G. Ivanov, Hongli Yang
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Lipschitz Extensions to Finitely Many Points
Analysis and Geometry in Metric Spaces, 2018 We consider Lipschitz maps with values in quasi-metric spaces and extend such maps to finitely many points. We prove that in this context every 1-Lipschitz map admits an extension such that its Lipschitz constant is bounded from above by the number of ...
Basso Giuliano
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