Positive solutions to \(X=A-BX^{-1}B^*\)
From MaRDI portal
Publication:914788
DOI10.1016/0024-3795(90)90005-WzbMath0702.15009MaRDI QIDQ914788
T. D. Morley, William N. jun. Anderson, George E. Trapp
Publication date: 1990
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Matrix equations and identities (15A24) Positive matrices and their generalizations; cones of matrices (15B48)
Related Items
Towards positive definite solutions of a class of nonlinear matrix equations ⋮ A survey on operator monotonicity, operator convexity, and operator means ⋮ On the Hermitian positive definite solutions of nonlinear matrix equation \(X^s + \sum_{i = 1}^m A_i^\ast X^{- t_i} A_i = Q\) ⋮ 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 $X-A^*X^{-1}A=Q$ ⋮ On the Matrix EquationX = Q − S∗X†S ⋮ The iterative method for solving nonlinear matrix equation \(X^{s} + A^{*}X^{-t}A = Q\) ⋮ Computations with infinite Toeplitz matrices and polynomials ⋮ Contractive maps on normed linear spaces and their applications to nonlinear matrix equations ⋮ Structure-Preserving Flows of Symplectic Matrix Pairs ⋮ Improved methods and starting values to solve the matrix equations $X\pm A^*X^{-1}A=I$ iteratively ⋮ Some investigation on Hermitian positive-definite solutions of a nonlinear matrix equation ⋮ On iterative algorithm and perturbation analysis for the nonlinear matrix equation ⋮ Iterative methods for the extremal positive definite solution of the matrix equation \(X+A^{*}X^{-\alpha}A=Q\) ⋮ Positive definite solutions of the matrix equation \(X^r - \sum_{i = 1}^m A_i^{\ast} X^{- \delta_i} A_i = I\) ⋮ On the iterative method for the system of nonlinear matrix equations ⋮ Where is the nearest non-regular pencil? ⋮ On the matrix equation ⋮ An accelerated technique for solving the positive definite solutions of a class of nonlinear matrix equations ⋮ Some iterative methods for the largest positive definite solution to a class of nonlinear matrix equation ⋮ The iterative methods for solving nonlinear matrix equation \(X+A^\star X^{-1}A+B^{\star}X^{-1}B=Q\) ⋮ How to solve the matrix equation \(XA-AX=f(X)\) ⋮ On the first degree Fejér-Riesz factorization and its applications to \(X+A^{\ast}X^{-1}A=Q\) ⋮ On the positive definite solutions of the matrix equations \(X^{s}\pm A^{\text T} X^{-t} A=I_{n}\) ⋮ On the Hermitian positive definite solutions of nonlinear matrix equation \(X^s + A^\ast X^{-t_1} A + B^\ast X^{-t_2} B = Q\) ⋮ The inversion-free iterative methods for a system of nonlinear matrix equations ⋮ Structure-Preserving Doubling Algorithms That Avoid Breakdowns for Algebraic Riccati-Type Matrix Equations ⋮ Solving system of nonlinear matrix equations over Hermitian positive definite matrices ⋮ Some properties of the nonlinear matrix equation \(X^s + A^* X^{-t} A = Q\) ⋮ Shorts of block operators and infinite networks - a note on the shorted operator. II ⋮ Iterative algorithm for solving a system of nonlinear matrix equations ⋮ Positive definite solutions of the nonlinear matrix equation \(X + A^H\bar{X}^{-1}A = I\) ⋮ On the existence of Hermitian positive definite solutions of the matrix equation \(X^s+A^*X^{-t}A=Q\) ⋮ Solvability for a nonlinear matrix equation ⋮ Condition numbers for the nonlinear matrix equation and their statistical estimation ⋮ The structure-preserving doubling algorithms for positive definite solution to a system of nonlinear matrix equations ⋮ An accelerated technique for solving one type of discrete-time algebraic Riccati equations ⋮ A note on the fixed-point iteration for the matrix equations \(X \pm A^* X^{-1}A=I\) ⋮ On the Hermitian positive definite solution and Newton's method for a nonlinear matrix equation ⋮ On convergence of three iterative methods for solving of the matrix equation \(X+A^\ast X^{-1}A+B^\ast X^{-1}B=Q\) ⋮ Convergence analysis of some iterative methods for a nonlinear matrix equation ⋮ On Ando-Li-Mathias geometric mean equations ⋮ Positive definite solutions of the matrix equations \(X\pm A^{\ast}X^{-q} A=Q\) ⋮ Iterative methods for nonlinear matrix equations \(X+ A^{\star}X^{-\alpha}A = I\) ⋮ 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 the matrix equation \(X+A^{T} \root 2^m \of {X^{-1}}A+I\) ⋮ On the Hermitian positive definite solutions of nonlinear matrix equation \(X^s + A^*X^{-t}A = Q\) ⋮ A new inversion free iteration for solving the equation \(X + A^{\star} X^{-1} A = Q\) ⋮ On equations that are equivalent to the nonlinear matrix equation \(X+A^{*}X ^{-\alpha}A=Q\) ⋮ Numerical solution of a quadratic eigenvalue problem ⋮ On the Hermitian positive definite solution of the nonlinear matrix equation ⋮ Perturbation analysis of the maximal solution of the matrix equation \(X+A^*X^{-1}A=P\) ⋮ Generalized Schur complements and oblique projections ⋮ Unnamed Item ⋮ On the Hermitian positive defnite solution of the nonlinear matrix equation \(X + A^*X ^{-1} A + B^*X ^{-1} B = I\) ⋮ Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation \(X+A^*X^{-1}A=Q\) ⋮ Solution of a class of nonlinear matrix equations ⋮ Some investigation on Hermitian positive definite solutions of the matrix equation \(X^s+A^*X^{-t}A=Q\) ⋮ Solving two generalized nonlinear matrix equations ⋮ Positive Definite Solutions of Operator Equations X m + A * X − n A = I ⋮ An iterative method to solve a nonlinear matrix equation ⋮ Newton's iterative method to solve a nonlinear matrix equation ⋮ A two-sided iterative method for computing positive definite solutions of a nonlinear matrix equation ⋮ An algorithm for computing positive definite solutions of the nonlinear matrix equationX + A*X−1A = I ⋮ On positive definite solutions of the nonlinear matrix equation \(X+A^* X^{-n} A=I\) ⋮ The inversion-free iterative methods for solving the nonlinear matrix equation \(X + A^H X^{- 1} A + B^H X^{- 1} B = I\) ⋮ On the matrix equation \(X+A^ TX^{-1}A=I\) ⋮ Hermitian solutions of the equation \(X=Q+NX^{-1}N^*\) ⋮ The inverse mean problem of geometric mean and contraharmonic means ⋮ On the positive definite solutions of nonlinear matrix equation \(X+A^*x^{-\delta}A=Q\). ⋮ SOME ITERATIVE ALGORITHMS FOR POSITIVE DEFINITE SOLUTION TO NONLINEAR MATRIX EQUATIONS ⋮ Properties of positive definite solutions of the equation \(X+A^*X^{-2}A=I\) ⋮ On nonlinear matrix equations \(X\pm\sum_{i=1}^{m}A_{i}^{*}X^{-n_{i}}A_{i}=I\) ⋮ Some properties for the existence of a positive definite solution of matrix equation \(X+A^*X^{-2^m}A=I\) ⋮ Inequalities for the eigenvalues of the positive definite solutions of the nonlinear matrix equation ⋮ On the nonlinear matrix equation \(X+A^*{\mathcal F}(X)A=Q\): solutions and perturbation theory
Cites Work
- Ladder networks, fixpoints, and the geometric mean
- An explicit linear solution for the quadratic dynamic programming problem
- Schur complements and statistics
- Functional calculus for sesquilinear forms and the purification map
- Means of positive linear operators
- Hermitian semidefinite matrix means and related matrix inequalities—an introduction
- Stabilizability of Linear Systems Over a Commutative Normed Algebra with Applications to Spatially-Distributed and Parameter-Dependent Systems
- A Note on the Shorted Operator
- Characterization of parallel subtraction
- Nonuniform Semi-Infinite Grounded Grids
- Shorted Operators. II
- Generalized Inverse Formulas Using the Schur Complement
- Consistent Estimates of the Parameters of a Linear System
- Shorted Operators
- Remarks on the Control of Discrete-Time Distributed Parameter Systems
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item