On the nonlinear matrix equation \(X+A^*{\mathcal F}(X)A=Q\): solutions and perturbation theory
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Publication:1602985
DOI10.1016/S0024-3795(01)00508-0zbMath1086.15013MaRDI QIDQ1602985
Martine C. B. Reurings, André C. M. Ran
Publication date: 24 June 2002
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
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Cites Work
- Positive solutions to \(X=A-BX^{-1}B^*\)
- Properties of positive definite solutions of the equation \(X+A^*X^{-2}A=I\)
- Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation \(X+A^*X^{-1}A=Q\)
- On an Iteration Method for Solving a Class of Nonlinear Matrix Equations
- On matrix equations \(X\pm A^*X^{-2}A=I\)
- Unnamed Item
- Unnamed Item
- Unnamed Item
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