Perturbation analysis of the matrix equation \(X=Q+A^{\text H}(\widehat X-C)^{-1}A\)

DOI10.1016/S0024-3795(03)00491-9zbMath1032.15009MaRDI QIDQ1410709

Ji-guang Sun

Publication date: 15 October 2003

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

zbMATH Keywords

numerical examplescondition numbermaximal solutionnonlinear matrix equationperturbation boundresidual bound

Mathematics Subject Classification ID

Related Items (6)

Positive definite solution of the matrix equation \(X=Q+A^{H}(I\otimes X-C)^{\delta}A\) ⋮ Existence and uniqueness of the positive definite solution for the matrix equation \(X=Q+A^\ast(\hat{X}-C)^{-1}A\) ⋮ Perturbation analysis of a quadratic matrix equation associated with an \(M\)-matrix ⋮ Perturbation analysis of an eigenvector-dependent nonlinear eigenvalue problem with applications ⋮ On the perturbation analysis of the maximal solution for the matrix equation \(X - \sum\limits_{i=1}^m A_i^\ast X^{-1} A_i + \sum\limits_{j=1}^n B_j^\ast X^{-1} B_j = I\) ⋮ A fixed point theorem for monotone maps and its applications to nonlinear matrix equations

Cites Work

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• Condition numbers of algebraic Riccati equations in the Frobenius norm
• On the Singular “Vectors” of the Lyapunov Operator
• The symmetric linear matrix equation
• Perturbation Theory for Algebraic Riccati Equations
• A Theory of Condition

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