Solutions and perturbation analysis for the nonlinear matrix equation \(X + \sum^m_{i=1} A^*_i X^{-1} A_i = I\)
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Publication:427002
DOI10.1016/j.amc.2011.10.026zbMath1250.15021OpenAlexW2184890300MaRDI QIDQ427002
Xue-Feng Duan, Chun-Mei Li, An-Ping Liao
Publication date: 13 June 2012
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2011.10.026
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Cites Work
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- Perturbation bounds for the Cholesky and QR factorizations
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- Solutions and perturbation estimates for the matrix equation \(X^s+A^*X^{-t}A=Q\)
- Iterative methods for the extremal positive definite solution of the matrix equation \(X+A^{*}X^{-\alpha}A=Q\)
- On the nonlinear matrix equation \(X - \sum_{i=1}^{m}A_{i}^{*}X^{\delta _{i}}A_{i} = Q\)
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- A note on the fixed-point iteration for the matrix equations \(X \pm A^* X^{-1}A=I\)
- A new inversion-free method for a rational matrix equation
- On the Hermitian positive definite solution of the nonlinear matrix equation
- Some investigation on Hermitian positive definite solutions of the matrix equation \(X^s+A^*X^{-t}A=Q\)
- On the existence of a positive definite solution of the matrix equation \(X+A^ T X^{-1} A=I\)
- On the positive definite solutions of the matrix equations \(X^{s}\pm A^{\text T} X^{-t} A=I_{n}\)
- Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation \(X+A^*X^{-1}A=Q\)
- On the nonlinear matrix equation \(X+A*X - qA=Q\) \((q\geq 1)\)
- On positive definite solutions of the family of matrix equations \(X+A^*X^{-n}A=Q\).
- On the matrix equation \(X+A^ TX^{-1}A=I\)
- On an Iteration Method for Solving a Class of Nonlinear Matrix Equations
- Iterative solution of two matrix equations
- Efficient computation of the extreme solutions of $X+A^*X^{-1}A=Q$ and $X-A^*X^{-1}A=Q$
- Improved methods and starting values to solve the matrix equations $X\pm A^*X^{-1}A=I$ iteratively
- Perturbation analysis of the maximal solution of the matrix equation \(X+A^*X^{-1}A=P\)
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