Necessary and sufficient conditions for the existence of positive definite solutions of the matrix equationX+ATX−2A=I

DOI10.1080/00207160412331336107zbMath1083.15020OpenAlexW2099296436MaRDI QIDQ5466769

Mohamed A. Ramadan

Publication date: 25 August 2005

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160412331336107

zbMATH Keywords

finite-difference approximationmatrix equationmatrix decompositionelliptic differential equationpositive definite solution

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Matrix equations and identities (15A24) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (12)

Investigation of the existence and uniqueness of extremal and positive definite solutions of nonlinear matrix equations ⋮ On the perturbation estimates of the maximal solution for the matrix equation \(X + A^T \sqrt{X^{- 1}} A = P\) ⋮ On the nonlinear matrix equation \(X+A*X - qA=Q\) \((q\geq 1)\) ⋮ The Hermitian positive definite solution of the nonlinear matrix equation ⋮ Necessary and sufficient conditions for the existence of a positive definite solution for the matrix equation \(X + \sum^m_{i = 1} A^T_i X^{\delta_i} A_i = I\) ⋮ On the existence of extremal positive definite solutions of the nonlinear matrix equation ⋮ The anti-symmetric solution of the matrix equation \(AXA^{\top} =B\) on a null subspace ⋮ Iterative solutions to coupled Sylvester-transpose matrix equations ⋮ An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices ⋮ On the matrix equation \(X+A^{T} \root 2^m \of {X^{-1}}A+I\) ⋮ ON THE MATRIX EQUATIONS Y \pm B^{T}e^{-Y}B=I ⋮ On solution and perturbation estimates for the nonlinear matrix equation \(X-A^*e^XA=I\)

Cites Work

• Matrix computations.
• Properties of positive definite solutions of the equation \(X+A^*X^{-2}A=I\)
• On the existence of a positive definite solution of the matrix equation \(X+A^ T X^{-1} A=I\)
• On the matrix equation \(X+A^ TX^{-1}A=I\)
• Iterative solution of two matrix equations
• On the existence of a positive definite solution of the matrix equation
• Efficient computation of the extreme solutions of $X+A^*X^{-1}A=Q$ and $X-A^*X^{-1}A=Q$
• Computing the Extremal Positive Definite Solutions of a Matrix Equation
• On matrix equations \(X\pm A^*X^{-2}A=I\)
• Perturbation analysis of the maximal solution of the matrix equation \(X+A^*X^{-1}A=P\)

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