P. Ataei Delshad - Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran.
T. Lotfi - Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran.

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.

Matrix sign function, Kung-Traub method, Algebraic Riccati equation, Stable Sylvester ‎equation.‎