Perturbation analysis of the Hermitian positive definite solution of the matrix equation \(X-A^{\ast}X^{-2} A = I\)

DOI10.1016/j.laa.2004.05.013zbMath1063.15010OpenAlexW2046958034MaRDI QIDQ1765886

Mingsong Cheng, Shu-fang Xu

Publication date: 23 February 2005

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

Full work available at URL: https://doi.org/10.1016/j.laa.2004.05.013

zbMATH Keywords

condition numberperturbation boundnonlinear matrix equationsnumerical examples.

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Conditioning of matrices (15A12)

Related Items (12)

Contractive maps on normed linear spaces and their applications to nonlinear matrix equations ⋮ The Hermitian positive definite solution of the nonlinear matrix equation ⋮ Positive fixed points for a class of nonlinear operators and applications ⋮ Positive definite solution of the matrix equation \(X=Q+A^{H}(I\otimes X-C)^{\delta}A\) ⋮ On the nonlinear matrix equation \(X - \sum_{i=1}^{m}A_{i}^{*}X^{\delta _{i}}A_{i} = Q\) ⋮ On positive definite solutions of nonlinear matrix equation \(X^s-A^{*}X^{-t}A=Q\) ⋮ Thompson metric method for solving a class of nonlinear matrix equation ⋮ Perturbation analysis of a quadratic matrix equation associated with an \(M\)-matrix ⋮ Solvability and sensitivity analysis of polynomial matrix equation \(X^s + A^TX^tA = Q\) ⋮ On Hermitian positive definite solution of the matrix equation \(X-\sum _{i=1}^mA_i^*X^r A_i = Q\) ⋮ Elementwise Minimal Nonnegative Solutions for a Class of Nonlinear Matrix Equations ⋮ On nonlinear matrix equations \(X\pm\sum_{i=1}^{m}A_{i}^{*}X^{-n_{i}}A_{i}=I\)

Cites Work

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• On the positive definite solutions of the matrix equations \(X^{s}\pm A^{\text T} X^{-t} A=I_{n}\)
• On the nonlinear matrix equation \(X+A^*{\mathcal F}(X)A=Q\): solutions and perturbation theory
• Perturbation analysis of the maximal solution of the matrix equation \(X+A^*X^{-1}A=P\). II
• On an Iteration Method for Solving a Class of Nonlinear Matrix Equations
• A Theory of Condition
• On matrix equations \(X\pm A^*X^{-2}A=I\)
• Two iteration processes for computing positive definite solutions of the equation \(X-A^*X^{-n}A=Q\)

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