An Accelerated Sixth-Order Procedure to Determine the Matrix Sign Function Computationally

The matrix sign function has a key role in several applications in numerical linear algebra. This paper presents a novel iterative approach with a sixth order of convergence to efficiently compute this function. The scheme is constructed via the employment of a nonlinear equations solver for simple roots. Then, the convergence of the extended matrix procedure is investigated to demonstrate the sixth rate of convergence. Basins of attractions for the proposed solver are given to show its global convergence behavior as well. Finally, the numerical experiments demonstrate the effectiveness of our approach compared to classical methods.