Positive definite solution of a class of nonlinear matrix equation

DOI10.1080/03081087.2013.794230zbMath1302.65099OpenAlexW2073702304MaRDI QIDQ5495761

Qing-Wen Wang, Chun-Mei Li, Xue-Feng Duan

Publication date: 7 August 2014

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081087.2013.794230

zbMATH Keywords

numerical examplestochastic controlerror estimationiterative methodnonlinear matrix equationstochastic algebraic Riccati equationpositive definite solution

Mathematics Subject Classification ID

Related Items (7)

On the positive definite solution of a class of pair of nonlinear matrix equations ⋮ On the matrix equation ⋮ Solution of a class of cross-coupled nonlinear matrix equations ⋮ Unnamed Item ⋮ A note on positive definite solution of matrix equationX+M^*X^–1M–N^*X^–1N=1 ⋮ Solution of a class of nonlinear matrix equations ⋮ Inequalities for the eigenvalues of the positive definite solutions of the nonlinear matrix equation

Cites Work

• On two perturbation estimates of the extreme solutions to the equations \(X \pm A^*X^{-1}A = Q\)
• On the existence of Hermitian positive definite solutions of the matrix equation \(X^s+A^*X^{-t}A=Q\)
• A note on the fixed-point iteration for the matrix equations \(X \pm A^* X^{-1}A=I\)
• A new inversion-free method for a rational matrix equation
• On Hermitian positive definite solutions of matrix equation \(X+A^{\ast} X^{-2} A=I\).
• Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation \(X+A^*X^{-1}A=Q\)
• Fixed point theorems in partially ordered metric spaces and applications
• Hermitian solutions of the equation \(X=Q+NX^{-1}N^*\)
• On an Iteration Method for Solving a Class of Nonlinear Matrix Equations
• A fixed point theorem in partially ordered sets and some applications to matrix equations
• Efficient computation of the extreme solutions of $X+A^*X^{-1}A=Q$ and $X-A^*X^{-1}A=Q$
• Improved methods and starting values to solve the matrix equations $X\pm A^*X^{-1}A=I$ iteratively
• Computing the Extremal Positive Definite Solutions of a Matrix Equation
• Perturbation analysis of the maximal solution of the matrix equation \(X+A^*X^{-1}A=P\)

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