Perturbation analysis of the matrix equation \(X-A^*X^{-p}A=Q\)

DOI10.1016/j.laa.2009.05.013zbMath1173.15006OpenAlexW2051155033MaRDI QIDQ840646

Jing Li, Yuhai Zhang

Publication date: 14 September 2009

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

Full work available at URL: https://doi.org/10.1016/j.laa.2009.05.013

zbMATH Keywords

numerical examplescondition numbernonlinear matrix equationperturbation boundpositive definite solutionbackward error

Mathematics Subject Classification ID

Related Items (10)

Positive definite solutions of the matrix equations ⋮ Solvability for a nonlinear matrix equation ⋮ Positive definite solutions and perturbation analysis of a class of nonlinear matrix equations ⋮ Solutions and improved perturbation analysis for the matrix equation \(X-A^\ast X^{-p}A=Q(p>0)\) ⋮ The investigation on two kinds of nonlinear matrix equations ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On the perturbation analysis of the maximal solution for the matrix equation \(X - \sum\limits_{i=1}^m A_i^\ast X^{-1} A_i + \sum\limits_{j=1}^n B_j^\ast X^{-1} B_j = I\) ⋮ Perturbation analysis of the nonlinear matrix equation \(X - \sum_{i = 1}^m A_i^* X^{p i} A_i = Q\) ⋮ Notes on the Hermitian positive definite solutions of a matrix equation

Cites Work

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• Properties of positive definite solutions of the equation \(X+A^*X^{-2}A=I\)
• On the existence of a positive definite solution of the matrix equation \(X+A^ T X^{-1} A=I\)
• On the positive definite solutions of the matrix equations \(X^{s}\pm A^{\text T} X^{-t} A=I_{n}\)
• On Hermitian positive definite solutions of matrix equation \(X+A^{\ast} X^{-2} A=I\).
• Improved perturbation estimates for the matrix equations \(X \pm A^{*} X^{-1} A=Q\).
• Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation \(X+A^*X^{-1}A=Q\)
• Perturbation analysis of the maximal solution of the matrix equation \(X+A^*X^{-1}A=P\). II
• Positive definite solutions of the matrix equations \(X\pm A^{\ast}X^{-q} A=Q\)
• On the matrix equation \(X+A^ TX^{-1}A=I\)
• Hermitian solutions of the equation \(X=Q+NX^{-1}N^*\)
• Iterative solution of two matrix equations
• Computing the Extremal Positive Definite Solutions of a Matrix Equation
• A Theory of Condition
• On matrix equations \(X\pm A^*X^{-2}A=I\)
• Perturbation analysis of the maximal solution of the matrix equation \(X+A^*X^{-1}A=P\)

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