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On certain classes of nonlinear matrix equations: theory, applications, and numerical solution

Bolletino Dell Unione Matematica Italiana
Some classes of nonlinear matrix equations, typically arising in queuing networks and Markov chain applications, are presented from a theoretical and computational perspective.
Beatrice Meini
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A Class of Matrix Ensembles

Journal of Mathematical Physics, 1972
A class of random matrix ensembles is defined, with the purpose of providing a realistic statistical description of the Hamiltonian of a complicated quantum-mechanical system (such as a heavy nucleus) for which an approximate model Hamiltonian is known.
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The Matrix Class B

Journal of Agriculture, Science and Technology, 2005
Keywords: banach spaces, Matrix, class BJAGST Vol 6(1) 2004: 69 ...
Mutekhele, JSK, Akanga, JR
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An introduction to a class of matrix cone programming

Mathematical Programming, 2012
A class of linear conic programming is defined (called matrix cone programming or MCP) involving the epigraphs of five commonly used matrix norms and the well studied symmetric cone. MCP has recently been found to have many important applications, for example, in nuclear norm relaxations of affine rank minimization problems. In order to make this class
Chao Ding, Defeng Sun, Kim-Chuan Toh
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A Special Class of Matrix in Three-Dimensional Combinatorial Matrix Class

2013
Two-dimensional combinatorial matrix class was found by Richard A Brandi in his book Combinatorial Matrix Class in 2006. In this book, he gave us the definition of this matrix, proves its existent theory, and analyzes its construction. In this paper, we define the three-dimensional combinatorial matrix (TDCM) class \( A(R,\,S,\,T) \) basic of two ...
Junna Jiang, Bing Han, Hong Wang
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Solving a class of quadratic matrix equations

Applied Mathematics Letters, 2018
The authors describe all commuting solutions (i.e., \(AX=XA\)) and, under a full rank condition, all non-commuting solutions, of the matrix equation \(AXA=XAX\), for a given invertible matrix \(A\).
Saeed Ibrahim Adam Mansour, Jiu Ding, Qianglian Huang, Lanping Zhu   +3 more
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A Combinatorial method for a class of matrix games

Journal of Applied Probability, 1966
The optimal strategies of any finite matrix game can be characterized by means of the Snow-Shapley Theorem [1]. However, in order to use this theorem to compute the optimal strategies, it may be necessary to invert a large number of matrices, most of which are not related to the solutions of the game.
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Combinatorial Matrix Classes

2006
A natural sequel to the author's previous book Combinatorial Matrix Theory written with H. J. Ryser, this is the first book devoted exclusively to existence questions, constructive algorithms, enumeration questions, and other properties concerning classes of matrices of combinatorial significance.
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A Class of Robustness Problems in Matrix Analysis

2002
We present an overview of several results and a literature guide, prove some new results, and state open problems concerning description of all robust matrices in the following sense: Let be given a class of real or complex matrices A, and for each X ∈ A, a set G(X) is given.
Ran, A.C.M., Rodman, L.
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Research on a Class of Nonlinear Matrix Equation

2014
In this paper, the nonlinear matrix equation \(X^{r}+\sum\limits_{i=1}^{m}A_{i}^{\ast}X^{\delta_{i}}A_{i}\) = Q is discussed. We propose the Newton iteration method for obtaining the Hermite positive definite solution of this equation. And a numerical example is given to identify the efficiency of the results obtained.
Jiating Fang, Haifeng Sang, Qingchun Li, Bo Wang   +3 more
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