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On the Positive Definite Solutions of a Nonlinear Matrix Equation [PDF]
Journal of Applied Mathematics, 2013 The positive definite solutions of the nonlinear matrix equation are discussed. A necessary and sufficient condition for the existence of positive definite solutions for this equation is derived.
Panpan Liu, Shugong Zhang, Qingchun Li
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Notes on the Hermitian Positive Definite Solutions of a Matrix Equation [PDF]
Journal of Applied Mathematics, 2014 The nonlinear matrix equation, X-∑i=1mAi*XδiAi=Q, with -1 ...
Jing Li, Yuhai Zhang
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On the positive definite solutions of a nonlinear matrix equation [PDF]
2012 4th Electronic System-Integration Technology Conference, 2012 In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case are discussed. An algorithm that avoids matrix inversion with the case is proposed.
Ming Hui Wang +2 more
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Hermitian metrics with (anti-)self-dual Riemann tensor [PDF]
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2021 Equations of (anti-)self-duality for the components of the LeviCivita connection of the Hermitian positive definite metric (not for the Riemann tensor) are compiled.
Leonid Krivonosov, Vyacheslav Luk'yanov
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Asymptotic behavior of solutions of fully nonlinear equations over exterior domains
Comptes Rendus. Mathématique, 2021 In this paper, we consider the asymptotic behavior at infinity of solutions of a class of fully nonlinear elliptic equations $F(D^2u)=f(x)$ over exterior domains, where the Hessian matrix $(D^2u)$ tends to some symmetric positive definite matrix at ...
Jia, Xiaobiao
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Journal of Inequalities and Applications, 2016 We consider two nonlinear matrix equations X r ± ∑ i = 1 m A i ∗ X δ i A i = I $X^{r} \pm \sum_{i = 1}^{m} A_{i}^{*}X^{\delta_{i}}A_{i} = I$ , where − 1 < δ i < 0 $- 1 < \delta_{i} < 0$ , and r, m are positive integers. For the first equation (plus case),
Abdel-Shakoor M Sarhan +1 more
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On strong solutions for positive definite jump diffusions
Stochastic Processes and their Applications, 2011 version to appear in Stochastic Processes and Their Applications ...
Mayerhofer, Eberhard +2 more
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Approximating Solutions of Matrix Equations via Fixed Point Techniques
Mathematics, 2021 The principal goal of this work is to investigate new sufficient conditions for the existence and convergence of positive definite solutions to certain classes of matrix equations.
Rahul Shukla +3 more
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Positive Definite Solutions of the Matrix Equation Xr-∑i=1mAi∗X-δiAi=I
Abstract and Applied Analysis, 2015 We investigate the nonlinear matrix equation Xr-∑i=1mAi∗X-δiAi=I, where r is a positive integer and δi∈(0,1], for i=1,2,…,m. We establish necessary and sufficient conditions for the existence of positive definite solutions of this equation.
Asmaa M. Al-Dubiban
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Iterative Algorithm for Solving a System of Nonlinear Matrix Equations
Journal of Applied Mathematics, 2012 We discuss the positive definite solutions for the system of nonlinear matrix equations and , where , are two positive integers. Some properties of solutions are studied, and the necessary and sufficient conditions for the existence of positive ...
Asmaa M. Al-Dubiban
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