On an iterative algorithm converging to the solution of XCX=D - Al-Harbi, Nawal; Raïssouli, Mustapha (Afrika mathematica, 2020)
Based on a modified Newton method in the Banach algebra of square matrices, we construct here a simple iterative algorithm that converges to the unique positive solution of the algebraic Riccati equation X C X = D . Numerical examples illustrating the theoretical study and showing the speed of convergence of our approach are discussed as well. At the end, we put some open questions as purposes for future research.