Perturbation analysis of the Hermitian positive definite solution of the matrix equation \(X-A^{\ast}X^{-2} A = I\)
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Publication:1765886
DOI10.1016/j.laa.2004.05.013zbMath1063.15010OpenAlexW2046958034MaRDI QIDQ1765886
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
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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