Positive definite solutions of the nonlinear matrix equation \(X+A^*X^qA=Q\) (\(q>0\)).
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Publication:547990
DOI10.1016/j.amc.2011.03.154zbMath1221.15026OpenAlexW158136187MaRDI QIDQ547990
Wei-wei Xie, Guo-Feng Zhang, Jing-yu Zhao
Publication date: 27 June 2011
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2011.03.154
eigenvaluenumerical examplesiterative methodFrobenius normpositive definite solutionsnonlinear matrix equationHermitian positive definite matrix
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Related Items (5)
Fixed point iterative methods for solving the nonlinear matrix equation \(X-A^*X^{-n}A=I\) ⋮ On positive definite solutions of the nonlinear matrix equations \(X \pm A^* X^q A = Q\) ⋮ The investigation on two kinds of nonlinear matrix equations ⋮ On solution and perturbation estimates for the nonlinear matrix equation \(X-A^*e^XA=I\) ⋮ Inequalities for the eigenvalues of the positive definite solutions of the nonlinear matrix equation
Cites Work
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- On the positive definite solutions of the matrix equations \(X^{s}\pm A^{\text T} X^{-t} A=I_{n}\)
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- Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation \(X+A^*X^{-1}A=Q\)
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- On an Iteration Method for Solving a Class of Nonlinear Matrix Equations
- Improved methods and starting values to solve the matrix equations $X\pm A^*X^{-1}A=I$ iteratively
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- Unnamed Item
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