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On iterative methods for the quadratic matrix equation with M-matrix

Applied Mathematics and Computation, 2011
The authors consider a kind of quadratic matrix equations (QME) arising from an overdamped vibrating system.Under the assumed \(M\)-matrix structure for the coefficient matrices the authors show that Newton's method and Bernoulli's method with an initial zero matrix converge nonincreasingly to the primary solvent of the QME.
Bo Yu 0022   +3 more
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Accurate solutions of M-matrix algebraic Riccati equations

Numerische Mathematik, 2011
This paper is concerned with the relative perturbation theory and its entrywise relatively accurate numerical solutions of an Riccati equation \(XDX-AX-B+C=0\), where the block-matrix \([{B\atop -C}{-D\atop A}]\) is a nonsingular or an irreducible singular \(M\)-matrix. Such Riccati equation has a unique nonnegative solution.
Jungong Xue, Shufang Xu, Ren-Cang Li
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On a quadratic matrix equation associated with an M-matrix

IMA Journal of Numerical Analysis, 2003
The main purpose of this work is to study the quadratic matrix equation \( X^{2}-EX-F=0\) where \(E,F,X\in \mathbb{R}^{n\times n}\), \(E\) is diagonal and \(F\) is an \( M\)-matrix. The main approach that the authors are using for solving the above quadratic matrix equation, is by transforming it into an equation that belongs to a special class of non ...
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M-Matrix Properties

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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PSD estimation in beamspace using property of M-matrix

2016 IEEE International Workshop on Acoustic Signal Enhancement (IWAENC), 2016
Microphone array Wiener filtering has been studied for practical sound source enhancement in noisy environments. In our previous work, the power spectral density (PSD)-estimation-in-beamspace method was proposed for estimating PSDs of target sources and surrounding noises. Assuming that source signals are uncorrelated with each other, the relationships
Kenta Niwa   +3 more
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Graphical solution of (n×m) matrix of a game theory

European Journal of Operational Research, 1999
Abstract Game theory deals with decisions under uncertainty involving two or more intelligent opponents in which each opponent aspires to optimise his own decision at the expense of the other opponents. To solve the matrix of game theory, graphical method is the easiest compared to other methods such as dominance property, matrix method etc.
Sanjay Kumar, D. S. N. Reddy
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An M-Matrix Theory and FD

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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K–M Matrix and Fermion Masses

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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Matrix viscoelasticity controls spatiotemporal tissue organization

Nature Materials, 2022
Alexander J Najibi   +2 more
exaly  

On the lower bounds for the minimum eigenvalue of the Hadamard product of an M-matrix and its inverse M-matrix

2012
Abstract: In this study, for the minimum eigenvalue 1()AAτ− of the Hadamard product 1AA− of an M-matrix A and its inverse1A− are considered. Some new lower bounds on 1()AAτ− for the Hadamard product of A and 1A− are derived. These bounds improve the results found in [H.B. Li, T.Z. Huang, S.Q. Shen, and H. Li.
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