Perturbation analysis for solutions of \(X \pm A^{\ast}X^{-n} A = Q\)
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Publication:1765925
DOI10.1016/j.laa.2004.08.017zbMath1076.15015OpenAlexW2093353166MaRDI QIDQ1765925
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.2004.08.017
Matrix equations and identities (15A24) Miscellaneous inequalities involving matrices (15A45) Numerical computation of matrix norms, conditioning, scaling (65F35)
Related Items (7)
Solutions and perturbation estimates for the matrix equation \(X^s+A^*X^{-t}A=Q\) ⋮ Contractive maps on normed linear spaces and their applications to nonlinear matrix equations ⋮ Condition numbers of the nonlinear matrix equation \(X^p - A^\ast e^X A = I\) ⋮ Condition numbers for the nonlinear matrix equation and their statistical estimation ⋮ On positive definite solutions of nonlinear matrix equation \(X^s-A^{*}X^{-t}A=Q\) ⋮ Newton's iterative method to solve a nonlinear matrix equation ⋮ On the matrix equation arising in an interpolation problem
Uses Software
Cites Work
- On the positive definite solutions of the matrix equations \(X^{s}\pm A^{\text T} X^{-t} A=I_{n}\)
- Improved perturbation estimates for the matrix equations \(X \pm A^{*} X^{-1} A=Q\).
- 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
- Solutions and perturbation estimates for the matrix equations \(X\pm A^*X^{-n}A=Q\)
- Perturbation analysis of the maximal solution of the matrix equation \(X+A^*X^{-1}A=P\)
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