The iterative methods for solving nonlinear matrix equation \(X+A^\star X^{-1}A+B^{\star}X^{-1}B=Q\)

DOI10.1186/1687-1847-2013-229zbMath1378.65109OpenAlexW3196820155WikidataQ59299466 ScholiaQ59299466MaRDI QIDQ1682174

Sarah Vaezzadeh, Seyyed Vaezpour Mansour, Reza Saadati, Chun-Gil Park

Publication date: 28 November 2017

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1847-2013-229

zbMATH Keywords

convergence ratenonlinear matrix equationpositive definite solutioninversion-free variant iterative method

Mathematics Subject Classification ID

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Cites Work

• A new inversion free iteration for solving the equation \(X + A^{\star} X^{-1} A = Q\)
• On the Hermitian positive defnite solution of the nonlinear matrix equation \(X + A^*X ^{-1} A + B^*X ^{-1} B = I\)
• Positive solutions to \(X=A-BX^{-1}B^*\)
• 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 \(X+A^*X^{-1}A=Q\)
• Vector optimization. Set-valued and variational analysis.
• On the matrix equation \(X+A^ TX^{-1}A=I\)
• On an Iteration Method for Solving a Class of Nonlinear Matrix Equations
• 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
• Computing the Extremal Positive Definite Solutions of a Matrix Equation
• On Direct Methods for Solving Poisson’s Equations
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