On the matrix equation arising in an interpolation problem
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Publication:2851009
DOI10.1080/03081087.2012.746326zbMath1288.15018OpenAlexW2026109545MaRDI QIDQ2851009
Qing-Wen Wang, An-Ping Liao, Xue-Feng Duan
Publication date: 1 October 2013
Published in: Linear and Multilinear Algebra (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/03081087.2012.746326
numerical exampleerror boundperturbation analysisnonlinear matrix equationfixed point iterationpositive definite solutionThompson metric
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Related Items (8)
Perturbation Theory for Linearly Perturbed Algebraic Riccati Equations ⋮ Positive definite solutions of the matrix equation \(X^r - \sum_{i = 1}^m A_i^{\ast} X^{- \delta_i} A_i = I\) ⋮ Positive definite solutions and perturbation analysis of a class of nonlinear matrix equations ⋮ The investigation on two kinds of nonlinear matrix equations ⋮ Notes on the Hermitian positive definite solutions of a matrix equation ⋮ Solvability theory and iteration method for one self-adjoint polynomial matrix equation ⋮ On nonlinear matrix equations \(X\pm\sum_{i=1}^{m}A_{i}^{*}X^{-n_{i}}A_{i}=I\) ⋮ Inequalities for the eigenvalues of the positive definite solutions of the nonlinear matrix equation
Cites Work
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- On the existence of Hermitian positive definite solutions of the matrix equation \(X^s+A^*X^{-t}A=Q\)
- A note on the fixed-point iteration for the matrix equations \(X \pm A^* X^{-1}A=I\)
- Solving the nonlinear matrix equation \(X = Q + \sum ^{m}_{i=1}M_{i}X^{\delta _{i}}M^{*}_{i}\) via a contraction principle
- 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.
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- Iterative solution of two matrix equations
- Efficient computation of the extreme solutions of $X+A^*X^{-1}A=Q$ and $X-A^*X^{-1}A=Q$
- Improved methods and starting values to solve the matrix equations $X\pm A^*X^{-1}A=I$ iteratively
- Invariant metrics, contractions and nonlinear matrix equations
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