On positive definite solutions of the nonlinear matrix equation \(X+A^* X^{-n} A=I\)

DOI10.1016/S0096-3003(03)00360-6zbMath1055.15022MaRDI QIDQ1826667

Salah M. El-Sayed, Asmaa M. Al-Dbiban

Publication date: 6 August 2004

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

zbMATH Keywords

convergencepositive definite solutionsnonlinear matrix equations

Mathematics Subject Classification ID

Related Items (20)

Solutions and perturbation estimates for the matrix equation \(X^s+A^*X^{-t}A=Q\) ⋮ On the positive definite solutions of a nonlinear matrix equation ⋮ On the nonlinear matrix equation \(X+A*X - qA=Q\) \((q\geq 1)\) ⋮ Iterative methods for the extremal positive definite solution of the matrix equation \(X+A^{*}X^{-\alpha}A=Q\) ⋮ The inversion-free iterative methods for a system of nonlinear matrix equations ⋮ Some properties of the nonlinear matrix equation \(X^s + A^* X^{-t} A = Q\) ⋮ On the existence of Hermitian positive definite solutions of the matrix equation \(X^s+A^*X^{-t}A=Q\) ⋮ The structure-preserving doubling algorithms for positive definite solution to a system of nonlinear matrix equations ⋮ On the Hermitian positive definite solution and Newton's method for a nonlinear matrix equation ⋮ Iterative methods for nonlinear matrix equations \(X+ A^{\star}X^{-\alpha}A = I\) ⋮ Two structure-preserving-doubling like algorithms for obtaining the positive definite solution to a class of nonlinear matrix equation ⋮ Positive definite solutions of the nonlinear matrix equation \(X+A^*X^qA=Q\) (\(q>0\)). ⋮ On equations that are equivalent to the nonlinear matrix equation \(X+A^{*}X ^{-\alpha}A=Q\) ⋮ On Hermitian positive definite solutions of a nonlinear matrix equation ⋮ Some investigation on Hermitian positive definite solutions of the matrix equation \(X^s+A^*X^{-t}A=Q\) ⋮ An iterative method to solve a nonlinear matrix equation ⋮ Newton's iterative method to solve a nonlinear matrix equation ⋮ The inversion-free iterative methods for solving the nonlinear matrix equation \(X + A^H X^{- 1} A + B^H X^{- 1} B = I\) ⋮ A fixed point theorem for monotone maps and its applications to nonlinear matrix equations ⋮ On nonlinear matrix equations \(X\pm\sum_{i=1}^{m}A_{i}^{*}X^{-n_{i}}A_{i}=I\)

Cites Work

• Unnamed Item
• 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 \(X+A^ T X^{-1} A=I\)
• Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation \(X+A^*X^{-1}A=Q\)
• Some properties for the existence of a positive definite solution of matrix equation \(X+A^*X^{-2^m}A=I\)
• 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

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