Developing a Stable Method for Computing the Matrix Sign Function with Applications to Algebraic Riccati and Sylvester Equations

This paper aims to propose a constructive methodology for determining the matrix sign function for a stable variant of the Kung-Traub method. It analytically shows that the new scheme is asymptotically stable. Different numerical experiments compare the new scheme's behavior with the existing matrix iteration of the same type. Finally, the given approach applies to solve the algebraic Riccati equation and the Sylvester equation.