Positive Definite Solutions of Operator Equations X m + A * X − n A = I
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Publication:4458108
DOI10.1080/0308108031000068958zbMath1046.47019OpenAlexW1992986826MaRDI QIDQ4458108
Publication date: 17 March 2004
Published in: Linear and Multilinear Algebra (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/0308108031000068958
Hilbert spaceiterative methodspositive operatorserror estimationsoperator equationisometric operators
Matrix equations and identities (15A24) Equations involving linear operators, with operator unknowns (47A62)
Related Items (11)
Solutions and perturbation estimates for the matrix equation \(X^s+A^*X^{-t}A=Q\) ⋮ Unnamed Item ⋮ A new fixed point theorem in \(G_b\)-metric space and its application to solve a class 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 \(X^s+A^*X^{-t}A=Q\) ⋮ On positive definite solutions of the nonlinear matrix equations \(X \pm A^* X^q A = Q\) ⋮ 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 positive definite solutions of the family of matrix equations \(X+A^*X^{-n}A=Q\). ⋮ Some investigation on Hermitian positive definite solutions of the matrix equation \(X^s+A^*X^{-t}A=Q\) ⋮ Newton's iterative method to solve a nonlinear matrix equation
Cites Work
- 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 \(X+A^*X^{-1}A=Q\)
- On matrix equations \(X\pm A^*X^{-2}A=I\)
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