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The Investigation on Two Kinds of Nonlinear Matrix Equations
Bulletin of the Malaysian Mathematical Sciences Society, 2018The authors consider the nonlinear matrix equations \(X+\sum _{i=1}^mB_i^*X^{t_i}B_i=I ...
Li, Jing, Zhang, Yuhai
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On positive definite solution of a nonlinear matrix equation
Numerical Linear Algebra with Applications, 2006AbstractIn this paper, some necessary and sufficient conditions for the existence of the positive definite solutions for the matrix equationX+A*X−αA=Qwith α ∈ (0, ∞) are given. Iterative methods to obtain the positive definite solutions are established and the rates of convergence of the considered methods are obtained. Copyright © 2006 John Wiley &
Zhen-Yun Peng, Salah M. El-Sayed
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On the Solution of a Nonlinear Matrix Equation Arising in Queueing Problems
SIAM Journal on Matrix Analysis and Applications, 1996The paper presents a new algorithm for computing the solution of a matrix equation arising in a wide class of queueing problems. The algorithm which under mild conditions generates a sequence of matrices converging quadratically, can be fully described in terms of simple operations between matrix power series, i.e., power series in \(z\) having matrix ...
BINI, DARIO ANDREA, MEINI, BEATRICE
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On an Iteration Method for Solving a Class of Nonlinear Matrix Equations
SIAM Journal on Matrix Analysis and Applications, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
El-Sayed, S.M., Ran, A.C.M.
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A further study on a nonlinear matrix equation
Japan Journal of Industrial and Applied Mathematics, 2020The authors consider the nonlinear matrix equation \(X^p = R + M^T(X^{-1}+B)^{-1}M,\) where \(p\) is a positive integer, \(M\) is an \(n\times n\) real matrix and \(R\) and \(B\) are symmetric positive semidefinite matrices. For \(p=1\), this is a simplified symmetric form of the discrete-time algebraic Riccati equation and may be solved by an ...
Meng, Jie +3 more
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Convergence Rate of an Iterative Method for a Nonlinear Matrix Equation
SIAM Journal on Matrix Analysis and Applications, 2001This paper deals with the matrix equation \(X+ A^* X^{-1}A= Q\), where \(A,Q\in C^{m\times m}\) with \(Q\) Hermitian positive definite and the maximal solution \(X\), is required. Recently, \textit{B. Meini} proposed an iterative method [Math. Comput. 71, No. 239, 1189-1204 (2002; Zbl 0994.65046)] and a convergence result for the case \(\rho(X^{-1}_+ A)
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Matrix computations and nonlinear equations
Numerical Linear Algebra with Applications, 2011Owe Axelsson, Xiaojun Chen 0001
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A discretization of the matrix nonlinear Schrödinger equation
Journal of Physics A: Mathematical and General, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Interaction of solitons in the matrix nonlinear Schrödinger equation
Applied Mathematics LetterszbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Nonlinear Matrix Equations and Population Dynamics
1997Classical models for the dynamics of biological populations, such as the famous logistic and Lotka-Volterra equations, involve population-level statistics and parameters. In the “structured” population models of this book, individual members of the population are classified in some manner, usually by means of certain physiological characteristics, and ...
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