A two-sided iterative method for computing positive definite solutions of a nonlinear matrix equation

DOI10.1017/S1446181100013201zbMath1054.65041MaRDI QIDQ4461783

Salah M. El-Sayed

Publication date: 18 May 2004

Published in: The ANZIAM Journal (Search for Journal in Brave)

zbMATH Keywords

numerical examplesnormal matrix

Mathematics Subject Classification ID

Related Items (8)

On the existence of a positive definite solution of the matrix equation ⋮ On an inversion-free algorithm for the nonlinear matrix problem Xα+A∗X−βA+B∗X−γB=I, ⋮ Positive definite solution of a nonlinear matrix equation ⋮ Positive definite solutions of the nonlinear matrix equation \(X + A^H\bar{X}^{-1}A = I\) ⋮ A new inversion free iteration for solving the equation \(X + A^{\star} X^{-1} A = Q\) ⋮ Two iteration processes for computing positive definite solutions of the equation \(X-A^*X^{-n}A=Q\) ⋮ An algorithm for computing positive definite solutions of the nonlinear matrix equationX + A*X⁻¹A = I ⋮ Properties of positive definite solutions of the equation \(X+A^*X^{-2}A=I\)

Cites Work

• Unnamed Item
• 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 the matrix equation \(X+A^ TX^{-1}A=I\)
• Iterative solution of two matrix equations
• Computing the Extremal Positive Definite Solutions of a Matrix Equation
• On Direct Methods for Solving Poisson’s Equations

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