On the existence of a positive definite solution of the matrix equation

DOI10.1080/00207160108805029zbMath0972.65030OpenAlexW2078303593MaRDI QIDQ4528031

Mohamed A. Ramadan, Salah M. El-Sayed

Publication date: 19 November 2001

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

Full work available at URL: https://doi.org/10.1080/00207160108805029

zbMATH Keywords

optimal controlconvergenceerror boundsiterative methodmatrix equation

Mathematics Subject Classification ID

Related Items (18)

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 \(X + A^T \sqrt{X^{- 1}} A = P\) ⋮ 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 ⋮ Positive definite solution of the matrix equation \(X=Q+A^{H}(I\otimes X-C)^{\delta}A\) ⋮ On positive definite solution of nonlinear matrix equations ⋮ Positive definite solutions of the matrix equations \(X\pm A^{\ast}X^{-q} A=Q\) ⋮ Iterative methods for nonlinear matrix equations \(X+ A^{\star}X^{-\alpha}A = I\) ⋮ On the matrix equation \(X+A^{T} \root 2^m \of {X^{-1}}A+I\) ⋮ A new inversion free iteration for solving the equation \(X + A^{\star} X^{-1} A = Q\) ⋮ Two iteration processes for computing positive definite solutions of the equation \(X-A^*X^{-n}A=Q\) ⋮ Solution of a class of nonlinear matrix equations ⋮ Necessary and sufficient conditions for the existence of positive definite solutions of the matrix equationX+A^TX⁻²A=I ⋮ On the perturbation analysis of the maximal solution for the matrix equation \(X - \sum\limits_{i=1}^m A_i^\ast X^{-1} A_i + \sum\limits_{j=1}^n B_j^\ast X^{-1} B_j = I\) ⋮ On Hermitian positive definite solution of the matrix equation \(X-\sum _{i=1}^mA_i^*X^r A_i = Q\) ⋮ An algorithm for computing positive definite solutions of the nonlinear matrix equationX + A*X⁻¹A = I ⋮ On solution and perturbation estimates for the nonlinear matrix equation \(X-A^*e^XA=I\)

Cites Work

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• Positive solutions to \(X=A-BX^{-1}B^*\)
• 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 \(X+A^ T X^{-1} A=I\)
• A direct method for solving circulant tridiagonal block systems of linear equations
• Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation \(X+A^*X^{-1}A=Q\)
• Recursive Algorithms for Solving a Class of Nonlinear Matrix Equations with Applications to Certain Sensitivity Optimization Problems
• A two-sided iterative method for computing positive definite solutions of a nonlinear matrix equation
• On Direct Methods for Solving Poisson’s Equations

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