On Positive Definite Solutions of Nonlinear Matrix Equation X - A*X(-1)A = I
نویسندگان
چکیده
منابع مشابه
On the Positive Definite Solutions of a Nonlinear Matrix Equation
The positive definite solutions of the nonlinear matrix equation Xs + A∗f(X)A = Q are discussed. A necessary and sufficient condition for the existence of positive definite solutions for this equation is derived.Then, the uniqueness of the Hermitian positive definite solution is studied based on an iterative method proposed in this paper. Lastly the perturbation analysis for this equation is di...
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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 i r δ > − are discussed. An algorithm that avoids matrix inversion with the case 1 0 i δ − < < is proposed. Keywords—Nonlinear matrix equation, Positive definite solution, The maximal-minimal solution, Iterative method, Free-inversion.
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In this paper we consider the positive definite solutions of nonlinear matrix equation X + A X−δA = Q, where δ ∈ (0, 1], which appears for the first time in [S.M. El-Sayed, A.C.M. Ran, On an iteration methods for solving a class of nonlinear matrix equations, SIAM J. Matrix Anal. Appl. 23 (2001) 632–645]. The necessary and sufficient conditions for the existence of a solution are derived. An it...
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In this paper, an efficient iterative method is presented to solve a new nonlinear matrix equation * r X A X A I with real matrices and r 1 . Some properties of the positive definite solutions for the nonlinear matrix equation are derived. Moreover, necessary and sufficient conditions for the existence of the positive definite solutions are derived. The error estimation of the iterative m...
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ژورنال
عنوان ژورنال: DEStech Transactions on Computer Science and Engineering
سال: 2019
ISSN: 2475-8841
DOI: 10.12783/dtcse/ammms2018/27210