Positive definite solution of the matrix equation \(X = Q - A{^*}X^{-1}A + B{^*}X^{- 1}B\) via Bhaskar-Lakshmikantham fixed point theorem
type: Item
instance of: scholarly article
title: Positive definite solution of the matrix equation \(X = Q - A{^*}X^{-1}A + B{^*}X^{- 1}B\) via Bhaskar-Lakshmikantham fixed point theorem
zbMATH Open document ID: 1264.15015
DOI: 10.1186/2251-7456-6-27
author: Maher Berzig
author: Xuefeng Duan
author: Bessem Samet
published in: Mathematical Sciences
publication date: 2013-06-10T00:00:00Z
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 6172187
zbMATH Keywords: nonlinear matrix equation
zbMATH Keywords: positive definite solution
zbMATH Keywords: sufficient condition
zbMATH Keywords: iterative method
zbMATH Keywords: error estimation
zbMATH Keywords: coupled fixed point
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1186/2251-7456-6-27
OpenAlex ID: W2125416370
Wikidata QID: Q59288367
cites work: Q4255599
cites work: Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation \(X+A^*X^{-1}A=Q\)
cites work: Positive definite solutions of the matrix equations \(X\pm A^{\ast}X^{-q} A=Q\)
cites work: Computing the Extremal Positive Definite Solutions of a Matrix Equation
cites work: On the solution of the rational matrix equation \(X=Q+LX^{ - 1}L^{T}\)
cites work: Hermitian solutions of the equation \(X=Q+NX^{-1}N^*\)
cites work: On the existence of a positive definite solution of the matrix equation \(X+A^ T X^{-1} A=I\)
cites work: On the matrix equation \(X+A^ TX^{-1}A=I\)
cites work: A note on the fixed-point iteration for the matrix equations \(X \pm A^* X^{-1}A=I\)
cites work: Iterative solution of two matrix equations
cites work: Improved methods and starting values to solve the matrix equations $X\pm A^*X^{-1}A=I$ iteratively
cites work: A new inversion-free method for a rational matrix equation
cites work: Efficient computation of the extreme solutions of $X+A^*X^{-1}A=Q$ and $X-A^*X^{-1}A=Q$
cites work: Perturbation analysis of the maximal solution of the matrix equation \(X+A^*X^{-1}A=P\)
cites work: On the existence of Hermitian positive definite solutions of the matrix equation \(X^s+A^*X^{-t}A=Q\)
cites work: On the positive definite solutions of the matrix equations \(X^{s}\pm A^{\text T} X^{-t} A=I_{n}\)
cites work: On the Hermitian positive definite solution of the nonlinear matrix equation
cites work: Improved Newton's method with exact line searches to solve quadratic matrix equation
cites work: On the nonlinear matrix equation \(X+A*X - qA=Q\) \((q\geq 1)\)
cites work: On the positive definite solutions of nonlinear matrix equation \(X+A^*x^{-\delta}A=Q\).
cites work: On positive definite solutions of the family of matrix equations \(X+A^*X^{-n}A=Q\).
cites work: Properties of positive definite solutions of the equation \(X+A^*X^{-2}A=I\)
cites work: On positive definite solution of a nonlinear matrix equation
cites work: Iterative methods for the extremal positive definite solution of the matrix equation \(X+A^{*}X^{-\alpha}A=Q\)
cites work: Comment to: ``Perturbation estimates for the nonlinear matrix equation \(X-A^\ast X^qA=Q (0<q<1)\)'' by G. Jia and D. Gao
cites work: Solving systems of nonlinear matrix equations involving Lipschitzian mappings
cites work: On the nonlinear matrix equation \(X - \sum_{i=1}^{m}A_{i}^{*}X^{\delta _{i}}A_{i} = Q\)
cites work: On an iteration method for solving a class of nonlinear matrix equations
cites work: Solving a class of matrix equations via the Bhaskar-Lakshmikantham coupled fixed point theorem
cites work: A fixed point theorem in partially ordered sets and some applications to matrix equations
cites work: Fixed point theorems in partially ordered metric spaces and applications
cites work: Positive solutions to periodic boundary value problems involving nonlinear operators of Meir-Keeler-type
cites work: An extension of coupled fixed point's concept in higher dimension and applications
cites work: Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces
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description: scientific article; zbMATH DE number 6172187