On the nonlinear matrix equation \(X - \sum_{i=1}^{m}A_{i}^{*}X^{\delta _{i}}A_{i} = Q\)
From MaRDI portal
Publication:927756
DOI10.1016/j.laa.2008.02.014zbMath1148.15012OpenAlexW1985594841MaRDI QIDQ927756
Bin Tang, Xue-Feng Duan, An-Ping Liao
Publication date: 9 June 2008
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.laa.2008.02.014
Lua error in Module:PublicationMSCList at line 37: attempt to index local 'msc_result' (a nil value).
Related Items (46)
Investigation of the existence and uniqueness of extremal and positive definite solutions of nonlinear matrix equations ⋮ Iterative approximation of fixed points of Prešić operators on partial metric spaces ⋮ An efficient algorithm for the reflexive solution of the quaternion matrix equation \(AXB + CX^HD = F\) ⋮ Solving a class of nonlinear matrix equations via the coupled fixed point theorem ⋮ 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 ⋮ Solving systems of nonlinear matrix equations involving Lipschitzian mappings ⋮ Positive fixed points for a class of nonlinear operators and applications ⋮ Necessary and sufficient conditions for the existence of a positive definite solution for the matrix equation \(X + \sum^m_{i = 1} A^T_i X^{\delta_i} A_i = I\) ⋮ Positive definite solutions of the matrix equation \(X^r - \sum_{i = 1}^m A_i^{\ast} X^{- \delta_i} A_i = I\) ⋮ Some generalized fixed point results in a \(b\)-metric space and application to matrix equations ⋮ Positive definite solutions of the matrix equations ⋮ On the existence of extremal positive definite solutions of the nonlinear matrix equation ⋮ First results in suprametric spaces with applications ⋮ A coincidence point theorem and its applications to fractional differential equations ⋮ Hybrid coupled fixed point theorems in metric spaces with applications ⋮ Existence of positive solutions for a singular Hessian equation with a negative augmented term ⋮ Solutions and perturbation analysis for the nonlinear matrix equation \(X + \sum^m_{i=1} A^*_i X^{-1} A_i = I\) ⋮ A Lipschitz constant formula for vector addition in cones with applications to Stein-like equations ⋮ Positive definite solution of the matrix equation \(X=Q+A^{H}(I\otimes X-C)^{\delta}A\) ⋮ Perturbation analysis for the matrix equation \(X - \sum^m_{i=1} A^\ast_i XA_i + \sum^n_{j=1} B^\ast_j XB_j = I\) ⋮ Positive definite solution of the matrix equation \(X = Q - A{^*}X^{-1}A + B{^*}X^{- 1}B\) via Bhaskar-Lakshmikantham fixed point theorem ⋮ On positive definite solution of nonlinear matrix equations ⋮ Solutions and improved perturbation analysis for the matrix equation \(X-A^\ast X^{-p}A=Q(p>0)\) ⋮ Thompson metric method for solving a class of nonlinear matrix equation ⋮ Solving a class of matrix equations via the Bhaskar-Lakshmikantham coupled fixed point theorem ⋮ The investigation on two kinds of nonlinear matrix equations ⋮ Unnamed Item ⋮ Solution of a class of cross-coupled nonlinear matrix equations ⋮ Solving the nonlinear matrix equation \(X = Q + \sum ^{m}_{i=1}M_{i}X^{\delta _{i}}M^{*}_{i}\) via a contraction principle ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Solution of a class of nonlinear matrix equations ⋮ The positive definite solution to a nonlinear matrix equation ⋮ Solvability for two forms of nonlinear matrix equations ⋮ Solving two generalized nonlinear matrix equations ⋮ Positive coincidence points for a class of nonlinear operators and their applications to matrix equations ⋮ Normwise, mixed and componentwise condition numbers of matrix equation X-∑_{i=1}^p A_i^T XA_i + ∑_{j=1}^q B_j^T XB_j = Q$ ⋮ Weakly homogeneous variational inequalities and solvability of nonlinear equations over cones ⋮ Iterative algorithm for solving a class of quaternion matrix equation over the generalized \((P, Q)\)-reflexive matrices ⋮ Comment on: ``Perturbation analysis of the nonlinear matrix equation \(X - \sum_{i = 1}^m A_i^* X^{p i} A_i = Q\) ⋮ Perturbation analysis of the nonlinear matrix equation \(X - \sum_{i = 1}^m A_i^* X^{p i} A_i = Q\) ⋮ On the matrix equation arising in an interpolation problem ⋮ Notes on the Hermitian positive definite solutions of a matrix equation ⋮ A fixed point theorem for monotone maps and its applications to nonlinear matrix equations ⋮ Applying fixed point methodologies to solve a class of matrix difference equations for a new class of operators
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the positive definite solutions of the matrix equations \(X^{s}\pm A^{\text T} X^{-t} A=I_{n}\)
- A nonlinear matrix equation connected to interpolation theory.
- Perturbation analysis of the Hermitian positive definite solution of the matrix equation \(X-A^{\ast}X^{-2} A = I\)
- Positive definite solutions of the matrix equations \(X\pm A^{\ast}X^{-q} A=Q\)
- On positive definite solutions of the family of matrix equations \(X+A^*X^{-n}A=Q\).
- Hermitian solutions of the equation \(X=Q+NX^{-1}N^*\)
- On an Iteration Method for Solving a Class of Nonlinear Matrix Equations
- Iterative solution of two matrix equations
- Existence and uniqueness of positive fixed points for mixed monotone operators and applications
- Improved methods and starting values to solve the matrix equations $X\pm A^*X^{-1}A=I$ iteratively
- Two kinds of nonlinear matrix equations and their corresponding matrix sequences
- Matrix inequalities
This page was built for publication: On the nonlinear matrix equation \(X - \sum_{i=1}^{m}A_{i}^{*}X^{\delta _{i}}A_{i} = Q\)
