An Accelerated Iterative Method to Find the Sign of a Nonsingular Matrix with Quartical Convergence

The function of matrix sign is one of the most significant functions of matrices with several applications. The target of this work is to propose a novel numerical scheme in the form of an iteration scheme for finding the sign of a nonsingular matrix with quartical convergence. The convergence is global and the coefficients of the method have been proposed so as to enlarge the associated basins of attraction when compared to the similar methods of the same order of convergence from literature. Ultimately, numerical results are furnished to support the analytical discussion.