The inversion-free iterative methods for solving the nonlinear matrix equation \(X + A^H X^{- 1} A + B^H X^{- 1} B = I\)
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Publication:2319179
DOI10.1155/2013/843785zbMath1470.65085OpenAlexW1529684579WikidataQ58917592 ScholiaQ58917592MaRDI QIDQ2319179
Publication date: 16 August 2019
Published in: Abstract and Applied Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1155/2013/843785
Related Items (4)
On an inversion-free algorithm for the nonlinear matrix problem Xα+A∗X−βA+B∗X−γB=I, ⋮ An efficient inversion-free method for solving the nonlinear matrix equation \(X^p + \sum_{j=1}^ma_j^*X^{-q_j}a_j=Q\) ⋮ The maximal positive definite solution of the nonlinear matrix equation \(X + A^*X^{-1}A+B^*X^{-1}B = I \) ⋮ Latest inversion-free iterative scheme for solving a pair of nonlinear matrix equations
Cites Work
- Unnamed Item
- On the iterative method for the system of nonlinear matrix equations
- On the Hermitian positive definite solutions of nonlinear matrix equation \(X^s + A^\ast X^{-t_1} A + B^\ast X^{-t_2} B = Q\)
- Complex symmetric stabilizing solution of the matrix equation \(X+A^{\top}X^{-1}A=Q\)
- A new inversion free iteration for solving the equation \(X + A^{\star} X^{-1} A = Q\)
- Positive definite solutions of the matrix equations
- On the Hermitian positive defnite solution of the nonlinear matrix equation \(X + A^*X ^{-1} A + B^*X ^{-1} B = I\)
- Iterative methods for the extremal positive definite solution of the matrix equation \(X+A^{*}X^{-\alpha}A=Q\)
- Positive solutions to \(X=A-BX^{-1}B^*\)
- A new inversion-free method for a rational matrix equation
- 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 \(X+A^*X^{-1}A=Q\)
- On positive definite solutions of the nonlinear matrix equation \(X+A^* X^{-n} A=I\)
- Solutions and perturbation estimates for the matrix equations \(X\pm A^*X^{-n}A=Q\)
- Iterative algorithm for solving a system of nonlinear matrix equations
- An improved inversion-free method for solving the matrix equation \(X + A^\ast X^{-{\alpha}}A = Q\)
- On the matrix equation \(X+A^ TX^{-1}A=I\)
- Hermitian solutions of the equation \(X=Q+NX^{-1}N^*\)
- On an Iteration Method for Solving a Class of Nonlinear Matrix Equations
- Perturbation Bounds for the Nonlinear Matrix Equation
- On a Nonlinear Matrix Equation Arising in Nano Research
- The Matrix Equation $X+A^TX^{-1}A=Q$ and Its Application in Nano Research
- Iterative solution of two matrix equations
- Efficient computation of the extreme solutions of $X+A^*X^{-1}A=Q$ and $X-A^*X^{-1}A=Q$
- Computing the Extremal Positive Definite Solutions of a Matrix Equation
- Convergence Analysis of Structure-Preserving Doubling Algorithms for Riccati-Type Matrix Equations
- Solution of the Matrix Equations $AX + XB = - Q$ and $S^T X + XS = - Q$
- Two iteration processes for computing positive definite solutions of the equation \(X-A^*X^{-n}A=Q\)
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